Question

If f(x)= sinx + 2x + 1, and g is the inverse function of f, what is the value of g'(1)?
I can derive the function and plug in 1, I just need to know how to find the inverse function of f. As far as I can see, swapping y for x and solving for y isn't going to work.

Answer 1

finding inverse function is not easy
its not possible most of the time

Answer 2

you don't have to find the inverse function here as the problem is about finding the "derivative of the inverse function", not about finding the "inverse function itself"

Answer 3

Oh... I can take the derivative first, can't I?

Answer 4

you may use this property of inverse functions :
\[g(f(x)) = x\]

Answer 5

since g is the inverse of f,
g eats f

Answer 6

take derivative with respective to x both sides and get :

\[g'(f(x)) f'(x) = 1\]

Answer 7

let \(x=0\) in above equation

Answer 8

So g'(1) x 3 = 1, so 1/3.

Answer 9

Huh.

Answer 10

Looks good!

Answer 11

My thanks. That's certainly some tricky stuff.

Answer 12

Indeed it is! yw :)