December 22, 2014

Homework Help: Calculus (Please check my work!)

Posted by Anonymous on Thursday, March 15, 2012 at 2:10pm.

Suppose that y = f(x) = x^2 - 4x + 4.
Then on any interval where the inverse function y = f-1(x) exists, thederivative of y = f-1(x) with respect to x is:
(Hint: x^2 - 4x + 4 can be factored and rewritten as "something" squared.)

Work thus far:
Okay, so I know that I can factor y to equal y = (x - 2)^2
Next, I can solve for the inverse function:
x = (y - 2)^2
sqrt(x) = y - 2
y = sqrt(x) + 2
Then, I can find the derivative:
y' = (1/2)x^(-1/2)

Now, my concern is that the question also hints to an implicit solution to this problem. Working out the problem implicitly, I get:
x = y^2 - 4x + 4
1 = 2y(dy/dx) - 4(dy/dx)
dy/dx = 1 / (2y - 4) where x and y satisfy the equation y = x^2 - 4x + 4.
Would this answer be correct, as well? Or should it be "where x and y satisfy the equation x = y^2 - 4y +4"?

Answer this Question

First Name:
School Subject:

Related Questions

Calculus (Derivatives of Inverse Functions) - Suppose f(x) = sin(pi cos(x)). On ...
Calculus, check my answers, please! 3 - Did I get these practice questions right...
pre calculus - Find the inverse of the function below. Graph the function below ...
calculus - Consider the function f(x)=3x^2 5x on the interval [-4,4]. Find the...
CALCULUS! - Consider the function f(x)=4x^32x on the interval [2,2]. Find the...
Calculus - The function f(x)=(x^4)-(10x^3)+(18x^2)-8 is continuous on the closed...
Calculus Please help! - Consider the function f(x)=4sqrt(x)+4 on the interval [2...
College Algebra - Find the inverse of the function below. Graph the function ...
Calculus - Solve the following initial value problem and determine the interval ...
calculus - Consider the function f(x)=6sqrt(x)+1 on the interval [3,5] . Find ...