hvacwk

2021-12-16

How do you find $(f\cdot g)\left(x\right)$ and $(g\cdot f)\left(x\right)$ and determine if the given functions are inverses of each other $f\left(x\right)={x}^{2}-3$ and $g\left(x\right)=\sqrt{x}+3$ ?

Timothy Wolff

Beginner2021-12-17Added 26 answers

To find $f\left(g\left(x\right)\right)$ and $g\left(f\left(x\right)\right)$ substitute, g(x) for x in f(x), and f(x) for x in g(x), respectively. If they are inverses, both substitutions will equal x.

Explanation:

$f\left(g\left(x\right)\right)={(\sqrt{x}+3)}^{2}-3$

$f\left(g\left(x\right)\right)=x+6\sqrt{x}+9-3$

$f\left(g\left(x\right)\right)=x+6\sqrt{x}+6$

$g\left(f\left(x\right)\right)=\sqrt{{x}^{2}-3}+3$

They are not inverses, because both cases must reduce to x.

Explanation:

They are not inverses, because both cases must reduce to x.

Ella Williams

Beginner2021-12-18Added 28 answers

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