Answered

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

Sagot :

MrRoyal

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]

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