Question

Find the inverse of the following function.

Answer 1

Option: B is the correct answer.

B.
`f^(-1)(x)=x^3-12`

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`

Answer 2

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