Question

This is for pre calculus, please help

Answer 1

The correct answer is:

`g(x) = x+1`

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`