Answer:
[tex]f(x) = h(g(x))[/tex]
Step-by-step explanation:
Given
[tex]f(x) = \sqrt{6x + 7}[/tex]
Required
Write as simpler function
Let
[tex]h(x) = \sqrt x[/tex]
[tex]g(x) = 6x + 7[/tex]
Apply composite function rule:
[tex]h(x) = \sqrt x[/tex]
[tex]h(g(x)) = \sqrt{g(x)}[/tex]
Substitute: [tex]g(x) = 6x + 7[/tex]
[tex]h(g(x)) = \sqrt{6x + 7}[/tex]
By comparison:
[tex]f(x) = h(g(x)) = \sqrt{6x + 7}[/tex]
So:
[tex]f(x) = h(g(x))[/tex]
Where:
[tex]h(x) = \sqrt x[/tex]
[tex]g(x) = 6x + 7[/tex]
