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

Answer 2

The inverse function of the given function is  $f^{-1} (x)$=∛-x-9.

The given function is f(x)=-x³-9.

How to find the inverse function?

To find the inverse of a function, write the function y as a function of x i.e. y = f(x) and then solve for x as a function of y.

Now, replace f(x)=y.

y=-x³-9

Interchange the variables.

That is, x=-y³-9

Solve for y.

That is, y³=-x-9

⇒y=∛-x-9

Solve for y and replace with $f^{-1} (x)$.

$f^{-1} (x)$=∛-x-9.

Therefore, the inverse function of the given function is  $f^{-1} (x)$=∛-x-9.

To learn more about the inverse function visit:

https://brainly.com/question/2541698.

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