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)= (3x-9)/(x+4)`

Step-by-step explanation

Given functions are.......

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

`g(x)= (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)((3)/(x^2-16))\\ \\ (f*g)(x)= [(x-3)(x-4)][(3)/((x+4)(x-4))]\\ \\ (f*g)(x)= (3(x-3))/(x+4) = (3x-9)/(x+4)`