# Derivative of an Inverse

## Homework Statement

Assume that the Derivative Rule for Inverses holds. Given that f(x) = x + f(x), and g(t) = f-1(t), which of the following is equivalent to g'(t)?
a. g'(t) = 1 + t2
b. g'(t) = 1 + t4
c. g'(t) = 1 + g(x)
d. g'(t) = 1 / (1 + t4)

## The Attempt at a Solution

This question popped up on my recent calc final and my friends and I cannot agree on what the answer is. I answered with C, and most of my friends answered D, arguing that the fraction makes it correct. Can somebody with more knowledge explain this to me? Thank you!

Dick
Homework Helper

## Homework Statement

Assume that the Derivative Rule for Inverses holds. Given that f(x) = x + f(x), and g(t) = f-1(t), which of the following is equivalent to g'(t)?
a. g'(t) = 1 + t2
b. g'(t) = 1 + t4
c. g'(t) = 1 + g(x)
d. g'(t) = 1 / (1 + t4)

## The Attempt at a Solution

This question popped up on my recent calc final and my friends and I cannot agree on what the answer is. I answered with C, and most of my friends answered D, arguing that the fraction makes it correct. Can somebody with more knowledge explain this to me? Thank you!

I don't think any functions satisfy f(x)=x+f(x). Can you correct the statement?

That was the function given to us on the test as best as I can remember. It might have been something like f(x)= x + f(x)^3, but definitely f(x) = x + f(x)

Dick