Question

Which function is the inverse of f(x) = -x3 − 9?

Answer 1

Answer:

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

Step-by-step explanation:

$f(x) = -x^3-9$

Put f(x) = y

$y = -x^3-9$

Interchange x and y

$x = -y^3-9$

Solve for y

$x = -y^3-9$

Add 9 to both sides

$-y^3 = x+9$

Divide both sides by -1

$y^3 = -x-9$

Take cube root to both sides

$y = \sqrt[3]{-x-9}$

Put $y = f^{-1}(x)$

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

$\rule[225]{225}{2}$

Hope this helped!

~AH1807