How do you find $f(g(-3))$ given $f(x)=2x-1$ and $g(x)=3x$ and $h(x)=x^2+1$ ?

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Answer 1 · 2017-10-08T12:57:49

See a solution process below:

First, find $g(-3)$ by substituting $color(red)(-3)$ for each occurrence of $color(red)(x)$ in $g(x)$ :

$g(color(red)(x)) = 3color(red)(x)$ becomes:

$g(color(red)(-3)) = 3 xx color(red)(-3)$

$g(color(red)(-3)) = -9$

Therefore: $f(g(-3)) = f(-9)$

Because $g(-3) = -9$ then f(g(-3)) = f(-9)#

To find $f(-9)$ we can substitute $color(red)(-9)$ for each occurrence of $color(red)(x)$ in $f(x)$

$f(color(red)(x)) = 2color(red)(x) - 1$ becomes:

$f(color(red)(-9)) = (2 xx color(red)(-9)) - 1$

$f(color(red)(-9)) = -18 - 1$

$f(color(red)(-9)) = -19$

$f(g(-3)) = -19$

How do you find f(g(-3))f(g(-3)) given f(x)=2x-1f(x)=2x-1 and g(x)=3xg(x)=3x and h(x)=x^2+1h(x)=x^2+1?