Inverse functions Definition and 103 Threads

Hey can you please help me with finding the inverse of these functions and a brief explanation for each: y= x^2 (x> or equal to 0) y= 2log(base 10) x y= log (base 10) x-1 I need to submit each function and their inverse functions in one graph (three graphs for each function)...

We have a formula for the derivative of an inverse function: dy/dx = 1/(dx/dy). Just how useful is it? Say we want to find the inverse of a complicated function, f(x), on an interval (a,b) on which f(x) is one-to-one. Can we use integration to find such a function? Example: Say we didn't...

Homework Statement The function g(x) = (x2/e) + 2 ln(x) - e on (0,infinity) is one-to-one. Evaluate g-1(2)Homework Equations Find x in terms of y. Then switch x and y. Plug in 2 to the new equation.The Attempt at a Solution I can think of no way to get x explicitly in terms of y. I...

Homework Statement Given the function f(x) = \frac{ax+b}{cx+d} where f: \mathbb{R} \backslash \left\{ \frac{-d}{c} \right\} \rightarrow \mathbb{R} show that f is either a constant or has an inverse function. I can see why this would be true. If a function takes all real numbers and returns...

Just want to check that i am doing this question correctly. f(x) = 2x+5 h(x) = 1/x , x \neq0 Find the inverse of fh(x) So first i found the function fh(x) 2*1/x+5 then let y = 2*1/x+5 , x \neq0 now this is the bit i can't rememeber how to do, when i try and...

Homework Statement Use the functions below to find the indicated value. Homework Equations f(x)=1/5x - 3 http://www.webassign.net/cgi-bin/symimage.cgi?expr=f%28x%29%20%3D%201%2F5%20x%20-%203 g(x)=x^2http://www.webassign.net/cgi-bin/symimage.cgi?expr=g%28x%29%20%3D%20x%5E2 (g^-1 o...

Homework Statement This isn't really a homework question, just a curiousity, but here goes. Is it possible to find every function that is its own inverse? That is, can we find all functions that fit the definition f(x) = f^{-1}(x) \forall x ? I can name two... f(x) = x and f(x) =...

Homework Statement f(22)=9 and f^-1(13)=7 find f^-1(9) and f(7) (given that these are 1-1 functions) Homework Equations What does this mean as the have not given the equations they used to find the values, i know inverse function is the function that can find the opposite of the...

Hi all, I'm trying to get to grips with the Frechet derivative, and whilst I think I've got all the fundamental concepts down, I'm having trouble evaluating some of the trickier limits I've come up against. The two I'm struggling with currently are the further derivatives of the functions...

Homework Statement Find the domain/range: 1)cos[arcsin(-2x)]=f(x) 2)sin[arccos(x)] + 2cos(arcsin(x)]=f(x) 3)sin[arccos(sin(arccos(x)))]Homework Equations arccos domain:{-1,1] range[0,pi] arcsin domain:{-1,1] range[-pi/2,pi/2] tan domain:{-infinity,infinity] range[-pi/2,pi/2] The Attempt at a...

Homework Statement 1) Given f(x)= .01x³ + .7x -2 . Approximate ƒ−1(3). 2)Given f(x) = (x³) / (x²+1) and g(x) = ƒ–1(x). Evaluate g'(2) The Attempt at a Solution 1) Would this be correct? 3=.01x^3 + .7x -2 But then, how would I find x at 3? 2) I am confused about going...

I'm trying to find the inverse of a function, for instance: f(x)=(2x+1)/(x-1) using Mathematica but it doesn't produce any answers. This is my input: > f(x)=(2x+1)/(x-1) > InverseFunction[f] The output is always something like: "InverseFunction[(1+2x)/(-1+x)]" So, does anyone...

Homework Statement Suppose g is a function with the property that g(x) \neq g(y) if x \neq y. Prove that there is a function f such that f \circ g = I Homework Equations A function is collection of ordered pairs with the property that if (a,b) and (a,c) are in the collection, then b =...

Hyperbolic and Inverse Trigonometric Functions How extensive is the use of hyperbolic and inverse trigonometric functions in upper-level calculus and mathematics? I've taken 3 semesters of calculus, and not one of my teachers has gone over hyperbolic functions, and barely touched on inverse...

Sorry if this is the wrong place for my question, I'm having difficulty on a conceptual level getting my head round inverse functions and compositions of functions in R^n. I'm failing to understand my lecture notes as a result. Suppose I have some function with domain R^n which maps to R^m...

Hello :smile: I was wondering if someone could check my working and answers to these three homework questions. I've done the inverse functions in class, but not the composite inverse functions, if that's what they're called. Homework Statement...

Homework Statement If: h(x) and g(x) are inverse functions, then g[h(3)] = h[g(3)] = Homework Equations my teacher has neglected, yet again, to teach us how to do this.. could someone please help me.. this is all he gave us.. no functions or anything else to plug the #'s into...

Inverse functions for f:R^m-->R^m , or f:X^m-->Y^m Hi: This is , I guess a technical question: Given f:R^m --->R^m ; f=(f_1(x_1,..,x_m),...,f_m(x_1,...,x_m)) Then I guess f^-1 (of course, assume f is 1-1.). Is given by a "pointwise" inverse , (right?) i.e...

Hi, given two functions f and g, is there any known condition under which the following is valid: (f \circ g^{-1}) = (f^{-1} \circ g) Basically I have to find out the requirements for f and g for which composition is commutative in respect to inversion.

Homework Statement Set f(x)=\int^{2x}_{1}\sqrt{16 + t^{4}}dt. A. Show that f has an inverse. B. Find (f^{-1})'(0). Homework Equations (f^{-1})'(x)=1/(f'(f^{-1}(x))) The Attempt at a Solution A. f'(x)=\sqrt{16 + t^{4}} >0, so f is always increasing, hence one-to-one. By definition...

what is the inverse of f(x)=-2/3(x+5)^2 - 5/3 so far i got x=-2/3(y+5)^2 -5/3 bring 5/3 over to x side x+5/3=-2/3(y+5)^2 although i know what to do, can someone just explain how they will go on from here

Please help me with these following problems: 1.)Indicate whether each of the following functions is invertible in the given interval. Explain a.) sech x on [0,infinity) b.) cos (ln x) on (O, e^pie] c.) e^(x^2) on (-1,2] 2.) Evaluate the following limits, justifying your answers...

Homework Statement Find the inverse equation (i.e. solve for x) y=(e^x)/(1+2e^x)2. The attempt at a solution e^x = y(1+2e^x) x = ln(y) + ln(1+2e^x) ? Profit! I can't figure out what to do with ln(1+2e^x) to get the x out of there so I can finish isolating x. I tried balancing it another way...

Homework Statement f(x) = x3+ x. Note that f(2) = 10. Find (f-1)`(10). Homework Equations The Attempt at a Solution Note that where I have written ` it denotes prime (as in the derivative of). - Switch the x and y variables. x= y3 + y - Differentiate implicitly 1= (3y2 +...

Does anyone know of an existing methodology for determining and proving whether or not a function has an inverse? Thanks.

In Micheal C. Gemignani, "Elementary Topology" in section 1.1 there is the following exercise 2) i) If f:S \rightarrow T and G: T \rightarrow W , then (g \circ f)^{-1}(A) = f^{-1}(g^{-1}(A)) for any A \subset W . I think the above is only true if A is in the image of g yet the book says...

hi there.. I want to know how to integrate inverse trigonometric functions?like inverse tanx for example? thanx a lot..I just want a brief explanation?

If you've already found that F(g(X))=X, is it necessarry to also prove that g(f(X))=X to know that you have inverse functions? Would there be a case where the first statement is true but the second is false?

We have y=f(x), and get the inverse by uing the first function and solving it for x and get x=g(y). (F and g are different functions.) Then we swap the name of x and y and we get y=g(x). Buw why can we do this when we want to find the inverse functions? If we got y=f(x) and want to find the...

Hi, I know that the range of an inverse function is the domain of the function, but how do you work it out if you don't know it? You could sketch a graph but doesn't that get tricky for hard complicated functions. For example: \frac{3x}{x+1} - \frac{x+7}{x^{2}-1}, x > 1 If i find the inverse...

[SOLVED] Inverse Functions What is the area of the largest triangle in the first quadrant with 2 sides on the axes and third side tangent to the curve y=e^-x

i want the most general solution for sin6x=sin4x-sin2x

[SOLVED] Question involving trigonometric identities and inverse functions Homework Statement http://img141.imageshack.us/img141/2651/quiz1question5zi8.jpg Homework Equations I've tried to combine the following known equations to come up with a solution: \frac{d}{dx}(sin^{-1}x) =...

Homework Statement Hello. My following problem is partially about the maths concept involved but is largely to do with what the question is actually asking? It's from an online quiz and a printscreen of it has been provided as an attachment. Homework Equations See attachments for the...

Homework Statement a sample problem: arcsin(-1/2) 2. The attempt at a solution do i look at the unit circle and find the y-coordinate or x-coordinate that has -1/2? i did ASTC, and figure that it'd be in either quad 3 or quad 4; to tell you the truth i don't understand how to use...

Homework Statement My textbook states that the inverse of a bijection is also a bijection and is unique. I understand how to show that the inverse would be a bijection and intuitively I understand that it would be unique, but I'm not sure how to show that part. Homework Equations...

Homework Statement Show that f and g are inverse functions (a) analytically and (b) graphically. f(x) = 5x+1 g(x) = (x-1)/5Homework Equations I've got (a), but I'm unsure at how to solve for (b).The Attempt at a Solution Here's my (a): f(g(x)) = 5(x-1/5) + 1 = x How do I solve graphically?

Homework Statement Find the inverse: y = (e^x)/(e^x + 1) Homework Equations The Attempt at a Solution I switched x with y and solved for y but I ended up getting lne^y - lnx = lne^y +ln1 and then -lnx= ln1

Please HELP...Differentiating Inverse Functions Homework Statement f(x) = x^3 + 2x - 1 when a=2 2. The attempt at a solution I thought you did... 1/(f '(f-1(x))) but I am not sure how to solve for x? 0=x^3 + 2x - 1 1=x^3 + 2x -1 I tried factoring but that did not work either.

If h(x)=(3x-5)/(7-2x) Find an expression for h^-1(x) Here's my attempt! y=(3x-5)/(7-2x) (swap x for y): x=(3y-5)/(7-2y) I've tried rearranging to find y in terms of x but I can't see how to do it! x(-2y)=(3y-5)/7 -2y=(3y-5)/7 -2y/3y=-5/x

how do i find f(x)^-1 of y=4x+9/2x-3 the answer in the back of the textbook is f(x)^-1=3x+9/2x-4

Hi everyone... I am currently teaching summer Precalculus at the University of New Hampshire, and I have come to the section on inverse functions. I have no problems relating the basic definitions: one-to-one, horizontal line test, etc., but I am looking for clarification on one point...

In one of my older threads, I posted the following: log_b (n) = x if and only if b ^ x = n, where b > 0, and b is not equal to one. It was said this defines logarithm as the inverse to exponential. I don't really see how that works here, I think it just shows how you write logarithms...

Ok here is teh question, there is parts a-e, i have a-d answered correctly, but am having trouble on e. Q: A function g is g(x)=4(x-3)^2 + 1 a) Graph g and the inverse of g. (Already completed) b) At what points do g and the inverse of g intersect. (completed) c) Determine an...

find the inverse of y= x + sinx i got as far as x=y+siny..but how do i get to y= ____? thanks

hey lads, i just was wondering if i solved this right: 5. Consider the function f(x) = 3x+cos(x), defined on the interval [0, pi] (a) prove that f has an inverse function g. Note: you are note expected to find the inverse function g indicate your reasoning. I dre the graph of f(x) and...

Could someone please explain to me how to work out the inverse function of a function? Please use the format f(x)=2e^2x + 4 as an example, if possible. thanks

I have a few problems that i need help with... Find the inverse of the function and verify that it is the inverse by performing a composition of functions both ways... 1. f(x) = (2x + 1) / (x + 3) when i interchange x and y.. i can't seem to solve for y... because i have a y in the...

closed form?? let f:u \rightarrow R^n be a differentiable function with a differentiable inverse f^{-1}: f(u) \rightarrow R^n . if every closed form on u is exact, show that the same is true for f(u). Hint: if dw=0 and f^{\star}w = d\eta, consider (f^{-1})^{\star}\eta. i don't...

find the inverse function of: f: [-1/2,infin) ---> R, Where F(x) = 3sqaureroot 2x+1 i got f(x) = 3squareroot 2x+1 x = 3squareroot 2(f-1)+1 f-1 = (x^3-1)/2 where (infin,-1/2] is this right? because when i graph it, it doesn't really look like the inverse also i...