Question

Find (f*g)(x) when f(x)=x^2-7x+12 and g(x)=3/x^2-16

Answer 1

The answer is:  $(f*g)(x)= \frac{3x-9}{x+4}$

Explanation

Given functions are.......

$f(x)=x^2-7x+12$

$g(x)= \frac{3}{x^2-16}$

For finding $(f*g)(x)$ , we just need to multiply the two functions $f(x)$ and $g(x)$. So......

$(f*g)(x)= f(x)*g(x)\\ \\ (f*g)(x)= (x^2-7x+12)(\frac{3}{x^2-16})\\ \\ (f*g)(x)= [(x-3)(x-4)][\frac{3}{(x+4)(x-4)}]\\ \\ (f*g)(x)= \frac{3(x-3)}{x+4} = \frac{3x-9}{x+4}$