Understanding the Derivative Rule for Inverses

[bang]

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)

Homework Equations

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 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)

Homework Equations

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?

 

[bang]

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]

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)

f(x)=x+f(x) means f(x)-f(x)=x. So x=0. It can't be an identity for the function f(x). Can you check with your classmates and figure out what the real question is?