Question

This is for pre calculus, please help

Answer 1

Answer:

The correct answer is:

$g(x) = x+1$

Step-by-step explanation:

Given that:

$h(x) = f\circ g(x)= \sqrt[3]{x+3}$

$f(x) = \sqrt[3]{x+2}$

To find:

$g(x) = ?$

Solution:

Let $g(x) = m$

We have

$f\circ g(x)= \sqrt[3]{x+3}\\OR\\f( g(x))= \sqrt[3]{x+3}$...... (1)

Now, we have let:

$g(x) = m\\\therefore f(g(x)) = f(m)$

Putting x = in f(x), we get

$f(x) = \sqrt[3]{x+2}\\\Rightarrow f(m) = \sqrt[3]{m+2}$....... (2)

Comparing equation (1) and (2):

$\sqrt[3]{x+3} =\sqrt[3]{m+2}$

Taking cubes both sides:

$x+3=m+2\\\Rightarrow m = x+3-2\\\Rightarrow m = x+1$

$\therefore g(x) = x+1$

Hence,

The correct answer is:

$g(x) = x+1$