If $f(x)=2x+8$ and $g(x)=3x-2$ , how do you find $g(f(-4))$ ?

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Answer 1 · 2018-04-07T15:38:44

$color(blue)(-2)$

First we find the function $g(f(x))$

To do this we substitute the variable $x$ in $g(x)$ for $f(x)$ :

$:.$

$g(x)=3x-2$

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

$f(x)=2x+8$

So:

$g(f(x))=3(2x+8)-2=6x+24-2=6x+22$

We now plug in the value $x=-4$

$g(f(-4))=6(-4)+22=color(blue)(-2)$

If f(x)=2x+8f(x)=2x+8 and g(x)=3x-2g(x)=3x-2, how do you find g(f(-4))g(f(-4))?