Question

Let f(x)=x2−9 ​ and g(x)=x2−7x+12 .

What is (fg)(x) ?




x−4/x+3 where ​ x≠−3,4 ​

x−4/x+3 where x≠−3,3

x+4/x−3 where ​ x≠−3,3 ​

x+3/x−4 where x≠3,4

Answer 1

`f(x)=x^2-9 , g(x)=x^2-7x+12`

We need to find
`(f)/(g)(x)`

`(f)/(g)(x)=(f(x))/(g(x))`

We replace f(x) and g(x)

`(f)/(g)(x)=(f(x))/(g(x))=(x^2-9)/(x^2-7x+12)`

Now factor the numerator and denominator and simplify it

`(x^2-9)/(x^2-7x+12)`

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

Cancel out x-3

`((x+3))/((x-4))` where x not equal to 3,4