# How do you find (g*h)(4) given f(x)=x^2-1 and g(x)=2x-3 and h(x)=1-4x#?

May 25, 2017

See a solution process below:

#### Explanation:

First, we can write $\left(g \cdot h\right) \left(x\right)$ as:

$\left(g \cdot h\right) \left(x\right) = \left(2 x - 3\right) \cdot \left(1 - 4 x\right)$

Next, we can substitute $\textcolor{red}{4}$ for each occurrence of $\textcolor{red}{x}$ in $\left(g \cdot h\right) \left(x\right)$ to find $\left(g \cdot h\right) \left(4\right)$:

$\left(g \cdot h\right) \left(\textcolor{red}{x}\right) = \left(2 \textcolor{red}{x} - 3\right) \cdot \left(1 - 4 \textcolor{red}{x}\right)$ becomes:

$\left(g \cdot h\right) \left(\textcolor{red}{4}\right) = \left(\left(2 \times \textcolor{red}{4}\right) - 3\right) \cdot \left(1 - \left(4 \times \textcolor{red}{4} x\right)\right)$

$\left(g \cdot h\right) \left(\textcolor{red}{4}\right) = \left(8 - 3\right) \cdot \left(1 - 16\right)$

$\left(g \cdot h\right) \left(\textcolor{red}{4}\right) = 5 \cdot - 15$

$\left(g \cdot h\right) \left(\textcolor{red}{4}\right) = - 75$