Question

Given: f(x) = 2x + 5 and g(x) = x 2 and h(x) = -2x h(g(f(x))) =

Answer 1

$\bf \begin{cases} f(x)=2x+5\\ g(x)=x^2\\ h(x)=-2x\\ ---------------\\ g(~~f(x)~~)=[f(x)]^2\\ \qquad \qquad \qquad [2x+5]^2\\ h(~~g(~~f(x)~~)~~)=-2~([2x+5]^2) \end{cases} \\\\\\ h(~~g(~~f(x)~~)~~)=-2(2x+5)(2x+5) \\\\\\ h(~~g(~~f(x)~~)~~)=-2(\stackrel{FOIL}{4x^2+20x+25}) \\\\\\ h(~~g(~~f(x)~~)~~)=-8x^2-40x-50$

Answer 2

A composite function is the combination of one or more functions.

The value of h(g(f(x))) is -4x -6

The given parameters are:

$f(x) = 2x + 5$

$g(x) = x - 2$

$h(x) = -2x$

We have:

$g(x) = x - 2$

Substitute f(x) for x

$g(f(x)) = f(x) -2$

Substitute $f(x) = 2x + 5$

$g(f(x)) = 2x + 5 -2$

$g(f(x)) = 2x + 3$

Substitute g(f(x)) for x in $h(x) = -2x$

$h(g(f(x))) = -2g(f(x))$

Substitute $g(f(x)) = 2x + 3$

$h(g(f(x))) = -2(2x + 3)$

Open bracket

$h(g(f(x))) = -4x -6$

Hence, the value of h(g(f(x))) is -4x -6

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