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03.07.2022 - 10:30

Use the pair of functions to find f (g (x)) and g (f (x)). Simplify your answers. f(x) = x^2 + 9, g (x) = square root {x + 2}

Question:

Use the pair of functions to find {eq}f (g (x)) {/eq} and {eq}g (f (x)) {/eq}. Simplify your answers.

{eq}\displaystyle f(x) = x^2 + 9, g (x) = sqrt {x + 2} {/eq}

Answers (1)

Louise April 8, 2023 в 01:04

To find {eq}f(g(x)){/eq}, we substitute {eq}g(x){/eq} into {eq}f(x){/eq} and simplify: {eq}begin{align*} f(g(x)) &= f(sqrt{x+2}) \ &= (sqrt{x+2})^2 + 9 \ &= x+11 end{align*}{/eq} Therefore, {eq}f(g(x))=x+11.{/eq} To find {eq}g(f(x)){/eq}, we substitute {eq}f(x){/eq} into {eq}g(x){/eq} and simplify: {eq}begin{align*} g(f(x)) &= sqrt{f(x)+2} \ &= sqrt{(x^2+9)+2} \ &= sqrt{x^2+11} end{align*}{/eq} Therefore, {eq}g(f(x))=sqrt{x^2+11}.{/eq}

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