Question

For the function f (x) = 3 (x + 7), find -1().

Answer 1

Given:

The function is
`f(x)=3(x+7)^{(1)/(4)}`.

To find:

The function
`f^(-1)(x)`.

Solution:

We have,

`f(x)=3(x+7)^{(1)/(4)}`

Substitute f(x)=y.

`y=3(x+7)^{(1)/(4)}`

Interchange x and y.

`x=3(y+7)^{(1)/(4)}`

Divide both sides by 3.

`(x)/(3)=(y+7)^{(1)/(4)}`

Taking power 4 on both sides.

`\left((x)/(3)\right)^4=y+7`

Subtract 7 from both sides.

`\left((x)/(3)\right)^4-7=y`

`y=\left((x)/(3)\right)^4-7`

Substitute
`y=f^(-1)(x)`.

`f^(-1)(x)=\left((x)/(3)\right)^4-7`

Therefore, the correct option is C.