Question

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

Answer 1

Answer:

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

Option B is correct option.

Step-by-step explanation:

We need to find inverse of $f(x)=-x^3-9$

For finding the inverse replace f(x) with y

$y=-x^3-9$

Now, solve for x

Adding 9 on both sides

$y+9=-x^3-9+9\\y+9=-x^3$

Multiply both sides by -1

$-(y+9)=x^3\\x^3=-y-9$

Taking cube root on both sides:

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

Now replace x with f^{-1}(x) and y with x

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

So, inverse of f(x)=-x^3-9 is $f^{-1}(x)=\sqrt[3]{-x-9}$

Option B is correct option.