Composite function Definition and 72 Threads

Homework Statement Hey, I've been working through a book and one problem just gets me that I know should be a piece of cake. I don't know if I'm just being an idiot or not seeing something but the problem is to take int e^(ax)cos(bx)dx and int e^(ax)sin(bx)dx simultaneously by multiplying the...

Homework Statement If lim f(x) as x->0 is = 0 then lim \frac{sin(f(x))}{f(x)} as x->0 = 1? dont know how to start proving this . thanks for the replies

1. Prove that (h\circ g)\circ f = h\circ (g\circ f) Homework Equations f:A\longmapsto B, g:B\longmapsto C, h:C\longmapsto D The Attempt at a Solution (h\circ g)\circ f =\{(b,d):d=h(c)\}\circ f =\{(b,d):d=h(g(b))\}\circ f I reach there and get stuck to continue...

Homework Statement I need to find functions f and g both continuouis at x = 0 for which the composite f at g is discontinuous at x = 0 Homework Equations The Attempt at a Solution I thnk it is a matter of looking for a composite function that results in 0 being in the...

Homework Statement Hi, I have trouble proving this claim and would really appreciate your help =). Thank you in advance! So here's the question: Suppose that f is a continuous function for all x>= 0 and differentiable for all x> 0. Also, f(0) = 0 and f' (1st derivative of f) is increasing on...

I'll be very thankful is someone will tell me where I'm wrong. We know: 1) f is uniform continuous. 2) g is uniform continuous. We want to prove: fg(x) is uniform continuous. proof: from 1 we know -> for every |a-b|<d_0 exists |f(a)-f(b)|<e from 2 we know -> for every |x-y|<d...

Homework Statement The sets A and B are defined respectively by A={x\in R : 0\leq x\leq 1} B={x\in R : 1\leq x\leq 2} and the functions f and g are defined respectively by f(x)=x^2-2x+2 g(x)=\frac{x+2}{x-1} where f(A)=B , g(B)=C with C as the range of the function g ...

i really need to see the proof of this theorem: if f and g are bijective then the inverse of (g o f) = inverse of f o inverse of g

Homework Statement let A,B,C be sets, and let f : A--> B and g : B--> C be functions. The composite function denoted by g o f is a function from A to C defined as follows: Homework Equations g o f(x)=g(f(x)) for every x in A. Prove that if g o f is one-to one, then f is one-to...

Homework Statement Given g(x)=|x| and f(x)=secx 1)Determine an equation for (f(g(x)) 2)State the domain 3)x and y intercepts 4)any asymptotes Homework Equations N/A The Attempt at a Solution f(g(x))=sec|x| or 1/cos|x|

Homework Statement Given the equation y= f(x) , at a certain point the slope of the curve is 1/2 and the x-coordinate decreases at 3 units/s. At that point, how fast is the y-coordinate of the object changing? The Attempt at a Solution Dy/dx = f ' (x) dx/dt Would that be...

Homework Statement The attempt at a solution g(f(x)) = h(x) 4f(x) + y = 4x - 1 4x + 16 + y = 4x - 1 y = -1 - 16 y = -17 so, g(x)= 4x + y = 4x - 17 Is this the correct way of going about this question? I used a guessing approach to this question. Is enough work shown to get...

Homework Statement If f(x) = x3+3x2+4x+5 and g(x)=5, then g(f(x)) = ? Homework Equations The Attempt at a Solution I don't know if I am correct. g(f(x)) = g(x3+3x2+4x+5)= 225? I plugged 5 into the equation. Am I right?

Homework Statement http://img171.imageshack.us/img171/543/pro3.png The Attempt at a Solution = f(g(h(x))) = f(g(\sqrt{x+3})) = f(cos\sqrt{x+3}) = \frac{2}{cos\sqrt{x+3}+1} Is this right, and am I showing enough work to get full marks? Do I need restrictions for example?

Homework Statement http://img21.imageshack.us/img21/8175/46521897.jpg The Attempt at a Solution I think I have a starting point, but I'm not 100% sure Basically I thought of just computing grad(f(α(t)) · dα/dt and showing its equal to zero. Am I on the right track, or shall I try...

Homework Statement Find the derivative of the function: cos(x)^(cos(cos(x))) Homework Equations The chain rule The Attempt at a Solution I know how the chain rule works, and I've done many problems with composite functions. However, I just don't know where to start with this one...

Homework Statement : discuss continuity of the composite function h(x)=f(g(x)) when A} F(x)=X^2 , g(x) = x-1 B} f(x) = 1/x-6 , g(x) = X^2+5 where should I start ?

Homework Statement Let f: X\rightarrowY and g: Y\rightarrowZ be functions. Prove or disprove the following: if g\circf is onto and g is one-to-one then f is onto. Homework Equations N/A The Attempt at a Solution I'm honestly not sure what to do with this. I believe that the...

Homework Statement “Geologist A” at the bottom of a cave signals to his colleague “Geologist B” at the surface by pushing a 11.0 kg box of samples from side to side. This causes a transverse wave to propagate up the 77.0 m rope. The total mass of the rope is 14.0 kg. Take g = 9.8 m/s². How...

Hello I have the following problem: Given two function f and g which are continuer on R, and some point c which belongs to R. I'm suppose to show that if f(c) = g(c), then h is continious on R. Isn't that the same as showing that that the composite function h(c) = g(f(c)) is...

What is the f, when f(f(x)) = 2x^2 - 1, Thanks alot! :confused:

my previous calculus teacher stressed finding the domain of a composite function; he stressed more of finding which areas were not part of the function by means of three circles and saying the function didn't pass to the other circle unless it met the range of the other function. The textbook...