Question

Im confused on how to work this out

Answer 1

If $f^{-1}(x)$ is the inverse of $f(x)$, then

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

Given $f(x)=x^3+9$, we have

$f\left(f^{-1}(x)\right) = \left(f^{-1}(x)\right)^3 + 9 = x$

Solve for the inverse :

$\left(f^{-1}(x)\right)^3 + 9 = x \\\\ \left(f^{-1}(x)\right)^3 = x-9 \\\\ \boxed{f^{-1}(x) = \sqrt[3]{x-9}}$

Your answer is incorrect because it's interpreted as "3 times the square root of (x - 9)", whereas you want to end up with "the cube root of (x - 9)".

Try inserting ∛(x - 9) or (x - 9)^(1/3).

Answer 2

Answer:

cube root (x-9)

Step-by-step explanation:

You have the right approach, but you wrote 3*square root(x-9)

What you need is cube root (x-9).