Inverse function Definition and 193 Threads

Homework Statement The function f is defined by y=f(x) = 3ln4x 0.01<=x<=1 a)Solve for x in terms of y and hence find the formula for the inverse function f^-1(x) b)Write down the domain of f^-1 c)Plot f from x =0.01 to x=1 and than plot f^-1 on the same axes but only for domain...

I've had a read through some of the topics about this but I am struggling to understand how to apply it. (1) Is it possible to apply the inverse function theorem to a function like f(x,y)=-xye(-(x^2+y^2)/2) or f(x,y)=2x^2+y^2-xy-7y (2) I am confused about how to compute the jacobian...

Homework Statement Let I be an interval in R, and let f: I-->R be one-to-one, continuous function. Then prove that f^(-1):f(I)-->R is also continuous. Homework Equations The Attempt at a Solution I started a thread yesterday and had some responses but the proofs became quite...

Homework Statement Given that f(x)=2x^3+5x+3 and f^-1(x)=1 then find the value of x Given that f(x)=x^3/(x^2+1) and f^-1(x)=2 then find the value of x Homework Equations I got to the eqn x=2Y^3+5Y+3 & X=Y^3/(Y^2+1) The Attempt at a Solution But now i m in trouble finding the...

Homework Statement \frac{\mathrm{d}\left(\frac{1}{a}\tan ^{-1} \left(\frac{x}{a}\right)\right)}{\mathrm{d}x}2. The attempt at a solution Let y = \frac{1}{a}\tan ^{-1} \left(\frac{x}{a}\right) \therefore x = a \tan \left(ay\right) Differentiate with respect to x \rightarrow 1 = a \sec ^2...

A friend of mine is tutoring a student in math, and they came across a problem that she couldn't answer. Here's a problem: both she and the student are Korean, and her English is okay, but not so good when it comes to specific terminology (like math). My Korean is very limited. The problem...

Homework Statement find (f-1)'(0) if f'(x) = root(1+x^4) The Attempt at a Solution i know (f-1)'(0) = 1 / f'((f-1 (0)) but to find the value of the inverse at 0, i need to find the inverse, for which i need to find the original function by integrating, and i cannot seem to be...

The function f is defined by f(x) = ln(4 - 2x), x<2, and x is a real number write down the domain of the inverse. I know that the domain of the inverse is the range of the function, but I am puzzled as to what that would be! Would it just be any real number? Thanks

Hello Integration is the 'area under the curve' for a one dimensional function. Say we have a function f(x)=x^2, if we compute the integral of this function between two limits we get the area under it between the two limits on the x axis. What if we wanted to find the area between two...

Hello: My 2 questions are underlined below. I have another problem but will first wait for an answer on this before posting the other question. Problem Statement Consider the function f:R2->R2 defined by f(x1,x2) = ( exp (x1-x2) + x^{2}_{1}x2 + x1(x2-1)^{4}...

Homework Statement Prove that the a continuous function with compact domain has a continuous inverse. Also prove that the result does not hold if the domain is not compact. Homework Equations The Attempt at a Solution I tried using the epsilon delta definition of continuity but...

Ok, I decided to review basic algebra since I haven't done anything with it in like, forever. I came across an inverse function problem that I can't get the right answer. the equation is: y = cuberoot(x+sqrt(1+x^2)) + cuberoot(x-sqrt(1+x^2)) I tried replacing X with Y, and solving for Y...

Ok, I decided to review basic algebra since I haven't done anything with it in like, forever. I came across an inverse function problem that I can't get the right answer. the equation is: y = cuberoot(x+sqrt(1+x^2)) + cuberoot(x-sqrt(1+x^2)) I tried replacing X with Y, and solving for Y...

Aye...title should say in R^2, sorry about that. I'm hitting somewhat of a wall in my understanding of a theorem (or rather a special case of a theorem). The theorem as stated in the book is as follows. The Inverse FUnction Theorem in the Plane Let O be an open subset of the plane R^2 and...

f(x) = ln(e^2x + e^x + 1) I want to find the inverse of this function. I get: e^y=e^2x + e^x + 1 If I say then that 1=e^0, then can I say y=2x + x? Therefore, x=y/3?

Hi I'm trying to remember inverse functions for calculus but I'm having a few problems. So any help would be appreciated. f(x)= 2x^3 + 3x^2 + 7x+ 4 So I have no clue how to solve this for the inverse. I know how to do basic ones. But I've forgotten these kind. So can i just get a step in...

Ok, We are asked to find (f-1(3))' for f(x) = 3 + x^2 + tan(x*pi/2) I think we are supposed to use the formula (f-1(x))' = 1/f'(f-1(x)) But I am not sure how to get f-1(3). If someone can show me how to get that, it would be extremely helpful for me to understand how this works...

from a graph of a function ( i obtained the graphg by doing a translation and y-scaling) g(x)= 1/3(x-2)^2 -3 b (x in [2:5]) i can see that g is increasing and so it is a one-one function and an image set is [-3;0]. so therefore the function g has an universe function g^-1 . so i can find...

Question: If g(x) = 5 + x + e^x, find g^-1(6) [inverse of g, not g to the power of -1] Attempted: So I first substitued g(x) to y So y = 5 + x + e^x then I tried isolating the x So y - 5 = x + e^x Then I applied ln to both sides ln(y) - ln(5) = ln(x) + ln(e^x) Due to the log rules...

What is the inverse of this function f(x) = x^3 + 2x? *************************************** f(x) = x^3 + 2x y = x^3 + 2x interchange x \Leftrightarrow y x = y^3 + 2y and it's a dead end to me ...

sin-(cos(7pi/5) (arcsin) i have the equation (x+n2pi) but don't know where to go from their

f(x) =2x + ln x f^-1(x)=? i do f(x)=2x +lnx=ln (e^2x) + ln x = ln [(e^2x)x] =>e^f(x)=e^2x(x)=> can eny body solve this equation

Dear All, Is it possible to have an analytical inverse function of y=x e^{-\frac{1}{x^2}}. Since y is monotonously increasing, its inverse function exists. But is it possible to get a close form? Thanks a lot! Phonic

So I need to find the derivative of the inverse function. I know that f is one-to-one and is continous. Also I know that f'(x)=1+[f(x)]^2. I found the inverse writing my equation like f(x)=x+(1/3)[f(x)]^3 then I switch the variables and get that my inverse function=(1/3)x^3 - x. Then I just take...

Im not sure whether this is a "Homework Question", but it is a question regarding the proof of the Inverse Function Theorem. It starts like this: Let k be the linear transformation Df(a). Then k is non-singular, since det(f '(a)) != 0. Now D((k^-1(f(a))) = D(k^-1)(f(a)) (Df(a)) = k^-1 (Df(a))...

Today I revised my knowledge from multivariable calculus and I found that I couldn't remember the proofs of these two theorems. Then I looked in Rudin, and everything was clear. Except one thing, which probably made me forgot the proofs. There are two weird functions in these two proofs...

I'm trying to see near which points of R^3 I can solve for theta, phi, and rho in terms of x,y, and z. I know i need to find the determinant and see when it equals zero; however, I get the determinant to equal zero when sin(phi) = 0, and when tan(theta) = -cot(phi). The first is right, but...

there have been a thread going on about worst/best notations. as i said there, i was confused with f^{-1}(x) when i first came across it in high school. i thought f^{-1}(x) is the same as {1}\over{f(x)} but now i am wondering, is there any function for which f^{-1}(x) = {1}\over{f(x)}?

Please, can you give me some hints about this? Here is a proof of the inverse function theorem. 1. After the statement and proof of a previous lemma, the author puts (L o f) as a composite function. I don't understand this because L is a matrix (the jacobian matrix of f(a) ) and I have...

If I have z=f(x,y), then how would I go about finding the inverse function? More specifically, say I have a parametric function of the form f(u,v) = (x(u,v), y(u,v),0) which is a coordinate transformation. How do I find the inverse of this function? All references I can find on...

let me start by saying that I'll be asking a lot of questions here soon as I'm preparing for a Calc BC AP test and I'm using practice exams to help. On the first practice exam, the first question: http://img390.imageshack.us/img390/9390/q1graph5bt.png Find the derivative of f^{-1}(x) at...

I can't seem to find the inverse to these two functions: f(x) = 3 + x^2 + tan(pi x/2) -1/x/1 f(x) = x^3 +x +1 I've tried manipulating these both for a half hour. But I havn't found the way to find the inverses of these. Any hints?

Hello, In this problem i have to find the inverse of the given function and the domain on which its valid. Here is the function f(x)= 1/(1+x) this is what i have done y= 1/(1+x) interchanging x and y x= 1/(1+y) y= (1/x)- 1 this is my inverse function. Now i need to...

Lately, we've been going over these two theorems in class. I have a few questions to put forth. 1) I know that in lower spaces, an inverse of a function exists locally (say around a point G) if it does not attain it's max/min at G (i.e. if f'(G) doesn't equal 0). Now, with the inverse...

how do I find the inverse function of y=xSqrt -2X I have tried transposing it 6 times now but my results don't give the right answer for a 1:1 function for x<0

Let f(x) = x^3 + e^x. Find (f^-1)'(2). I know how to do everything else except the first step. How do you find the inverse of f(x)? I know the inverse of an exponential function is a logarthmic function, but where do I proceed from here? Thanks.

Solve the following question. Give your answer in cert form .Thank you . sin-1 x + sin-1 (2x) = pie/3

I can only find two answers for this equation, whereas the books says it should be four. Can someone enlighten me? Showing the procedure would help:P (degrees) sec(2x+180) = 2 0<x<360

what is the inverse of of y=sqrt(x^3+x^2+x+1) i know u are suppose to solve for x but having trouble...help please

I have no idea how to do this question, can anyone provide some help? Suppose f is differentiable with derivative f '(x) = (1+x^3) ^(1/2). If g = f^-1, show that g ''(x) = 3/2 g(x)^2.

How do I find the inverse of the following function: f(x)= -3x^2 + 6x + 2 The answer is +/- sqrt( [2-x/3] +1 ) + 1 I have no idea how to get that answer. I tried switching x and y and solving for x but I can't get the answer. TiA.

I was just doing a problem in a review book and my answer doesn't match with what the books says. It f(x)=x^3+1 and if f^-1 is the inverse function of f, what is f^-1(4)? I got an answer of 0.02 but the book says it is 1.44. All I did was sub in 4 into the equation, which I get 64, then...

Could somebody please explain to me how you would calulate the inverse functions of x^3+4x+1. And if possible how you would calulate that on the TI-83 graphing calculator. Thanks