Question

Write f(x)=sprt(6x+7) as simpler function by introducing other function notations such as g(x) and h(x).

Answer 1

`f(x) = h(g(x))`

Explanation:

Given

`f(x) = √(6x + 7)`

Required

Write as simpler function

Let

`h(x) = \sqrt x`

`g(x) = 6x + 7`

Apply composite function rule:

`h(x) = \sqrt x`

`h(g(x)) = √(g(x))`

Substitute:
`g(x) = 6x + 7`

`h(g(x)) = √(6x + 7)`

By comparison:

`f(x) = h(g(x)) = √(6x + 7)`

So:

`f(x) = h(g(x))`

Where:

`h(x) = \sqrt x`

`g(x) = 6x + 7`