Question

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

Answer 1

Given:

The function is $f(x)=3(x+7)^{\frac{1}{4}}$.

To find:

The function $f^{-1}(x)$.

Solution:

We have,

$f(x)=3(x+7)^{\frac{1}{4}}$

Substitute f(x)=y.

$y=3(x+7)^{\frac{1}{4}}$

Interchange x and y.

$x=3(y+7)^{\frac{1}{4}}$

Divide both sides by 3.

$\dfrac{x}{3}=(y+7)^{\frac{1}{4}}$

Taking power 4 on both sides.

$\left(\dfrac{x}{3}\right)^4=y+7$

Subtract 7 from both sides.

$\left(\dfrac{x}{3}\right)^4-7=y$

$y=\left(\dfrac{x}{3}\right)^4-7$

Substitute $y=f^{-1}(x)$.

$f^{-1}(x)=\left(\dfrac{x}{3}\right)^4-7$

Therefore, the correct option is C.