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

Oct 8, 2017

See a solution process below:

#### Explanation:

First, find $g \left(- 3\right)$ by substituting $\textcolor{red}{- 3}$ for each occurrence of $\textcolor{red}{x}$ in $g \left(x\right)$:

$g \left(\textcolor{red}{x}\right) = 3 \textcolor{red}{x}$ becomes:

$g \left(\textcolor{red}{- 3}\right) = 3 \times \textcolor{red}{- 3}$

$g \left(\textcolor{red}{- 3}\right) = - 9$

Therefore: $f \left(g \left(- 3\right)\right) = f \left(- 9\right)$

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

To find $f \left(- 9\right)$ we can substitute $\textcolor{red}{- 9}$ for each occurrence of $\textcolor{red}{x}$ in $f \left(x\right)$

$f \left(\textcolor{red}{x}\right) = 2 \textcolor{red}{x} - 1$ becomes:

$f \left(\textcolor{red}{- 9}\right) = \left(2 \times \textcolor{red}{- 9}\right) - 1$

$f \left(\textcolor{red}{- 9}\right) = - 18 - 1$

$f \left(\textcolor{red}{- 9}\right) = - 19$

$f \left(g \left(- 3\right)\right) = - 19$