Question

Consider function f. f(x) = cube root of x - 7. Select g(x) so that f(g(x)) = g(f(x)) = x for all values of x.

Answer 1

The function g(x) is $g(x) = (x + 7)^3$

How to determine the function g(x)?

The function f(x) is given as:

$f(x) = \sqrt[3]{x} - 7$

If f(g(x)) = g(f(x)) = x, then the functions are inverse functions.

So, we have:

$f(x) = \sqrt[3]{x} - 7$

Rewrite as:

$y = \sqrt[3]{x} - 7$

Swap x and y

$x = \sqrt[3]{y} - 7$

Add 7 to both sides

$x + 7 = \sqrt[3]{y}$

Take the cube of both sides

$y = (x + 7)^3$

This implies that

$g(x) = (x + 7)^3$

Hence, the function g(x) is $g(x) = (x + 7)^3$

Read more about inverse functions at:

brainly.com/question/2541698

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