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

Jun 3, 2017

See a solution process below:

#### Explanation:

$\left(f \cdot g\right) \left(x\right) = \left({x}^{2} - 1\right) \left(2 x - 3\right)$

To multiply these two terms you multiply each individual term in the left parenthesis by each individual term in the right parenthesis.

$\left(f \cdot g\right) \left(x\right) = \left(\textcolor{red}{{x}^{2}} - \textcolor{red}{1}\right) \left(\textcolor{b l u e}{2 x} - \textcolor{b l u e}{3}\right)$ becomes:

$\left(f \cdot g\right) \left(x\right) = \left(\textcolor{red}{{x}^{2}} \times \textcolor{b l u e}{2 x}\right) - \left(\textcolor{red}{{x}^{2}} \times \textcolor{b l u e}{3}\right) - \left(\textcolor{red}{1} \times \textcolor{b l u e}{2 x}\right) + \left(\textcolor{red}{1} \times \textcolor{b l u e}{3}\right)$

$\left(f \cdot g\right) \left(x\right) = 2 {x}^{3} - 3 {x}^{2} - 2 x + 3$