Frank Guyton

2021-12-28

Find two functions $f\left(x\right)$ and $g\left(x\right)$ so that $h\left(x\right)=(f\circ g)\left(x\right)$

a)$h\left(x\right)={(2x+3)}^{2}$

b)$h\left(x\right)=\left|3-2x-{x}^{2}\right|$ .

c)$h\left(x\right)=h\left(x\right)=\frac{5}{\sqrt{3-x}}$

d)$h\left(x\right)=\sqrt{5}\{{x}^{3}+4{x}^{2}+1\}$

a)

b)

c)

d)

Buck Henry

Beginner2021-12-29Added 33 answers

Given data,

The function$h\left(x\right)$ is defined as $h\left(x\right)=fog\left(x\right)$

Step 1

a)Here,

$h\left(x\right)={(2x+3)}^{2}$

It is given that,

$h\left(x\right)=fog\left(x\right)$

By comparing both equations,

fοg$\left(x\right)={(2x+3)}^{2}$

$f\left(x\right)\times g\left(x\right)=(2x+3)\times (2x+3)$

The function

Step 1

a)Here,

It is given that,

By comparing both equations,

fοg

kaluitagf

Beginner2021-12-30Added 38 answers

b)Here,

$h\left(x\right)=\left|3-2x-{x}^{2}\right|$

It is given that,

$h\left(x\right)=f\text{\omicron g}\left(x\right)$

By comparing both equations,

fοg(x)f(x)×g(x)f(x)×g(x)Hence,

$\text{fog}\left(x\right)=\left|3-2x-{x}^{2}\right|$

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

$f\left(x\right)\times g\left(x\right)=\left|(-x+1)(x+3)\right|$

Hence,$f\left(x\right)=(1-x)$ and $g\left(x\right)=(x+3)$

It is given that,

By comparing both equations,

fοg(x)f(x)×g(x)f(x)×g(x)Hence,

Hence,

karton

Expert2022-01-09Added 613 answers

Step 2

c)Here,

It is given that,

By comparing both equations,

Hence,

Step 3

d)Here,

It is given that,

By comparing both equations,

Hence,

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