Suppose $f(x) = 3x+4.$ Then the inverse of $f$ is given by

$f^{-1}(x) =$ .

Moreover,

$f'(x) =$ , and

$\left(f^{-1}\right)'(x) =$ .

In general, if $f'(x) = A$, then

$\left(f^{-1}\right)'(f(x)) =$ (Note: Your answer must be in terms of $A$.)

Now let $f(x) = x + x^5.$ Then

$f(1) =$ ,

$f'(1) =$ ,

$f^{-1}(2) =$ , and

$\left(f^{-1}\right)'(2) =$ .

Notice that you can obtain the last two results without knowing a general expression for the inverse function of $f$. Indeed, if you feel enterprising try to come up with such an expression.