Question

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

Answer 1

Answer:

$f(x) = h(g(x))$

Step-by-step explanation:

Given

$f(x) = \sqrt{6x + 7}$

Required

Write as simpler function

Let

$h(x) = \sqrt x$

$g(x) = 6x + 7$

Apply composite function rule:

$h(x) = \sqrt x$

$h(g(x)) = \sqrt{g(x)}$

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

$h(g(x)) = \sqrt{6x + 7}$

By comparison:

$f(x) = h(g(x)) = \sqrt{6x + 7}$

So:

$f(x) = h(g(x))$

Where:

$h(x) = \sqrt x$

$g(x) = 6x + 7$