Question

Find the inverse of the following function.

Answer 1

For this case we must find the inverse of the following function:

$f (x) = \sqrt [3] {x + 12}$

For this, we follow the steps below:

Replace f (x) with y:

$y = \sqrt [3] {x + 12}$

We exchange the variables:

$x = \sqrt [3] {y + 12}$

We solve the equation for "and":

$\sqrt [3] {y + 12} = x$

We raise both sides of the equation to the cube to eliminate the root:

$(\sqrt [3] {y + 12}) = x ^ 3\\y + 12 = x ^ 3$

We subtract 12 on both sides of the equation:

$y = x ^ 3-12$

Thus, the inverse function is:

$f ^ {- 1} = x ^ 3-12$

Answer:

Option B

Answer 2

Answer:

Option: B is the correct answer.

       B.    $f^{-1}(x)=x^3-12$

Step-by-step explanation:

The inverse function f(x) is calculated in the following steps.

• Put  f(x)=y

• Interchange x and y in the equation.

• Now, solve for y.

The function f(x) is given by:

$f(x)=\sqrt[3]{x+12}$

Now, we keep:

$f(x)=y\\\\i.e.\\\\y=\sqrt[3]{x+12}$

Now, we interchange x and y

$x=\sqrt[3]{y+12}$

Now, on taking cube on both side of the equation we have:

$y+12=x^3\\\\i.e.\\\\y=x^3-12$

i.e.

$f^{-1}(x)=x^3-12$