Question

Find (f • g) when f(x) = x^2 + 5x + 6 and g(x) = 1/x+3

Answer 1

The correct option choice is D. 6x^2 + 41x + 70 / x^2 +6x + 9

Answer 2

option D

Explanation:

`f(x) = x^2 + 5x + 6`

`g(x)= (1)/(x+3)`

(fog)(x) = f(g(x))

Plug in g(x) in f(x)

We plug in 1/x+3 in the place of x in f(x)

`f(g(x))= f((1)/(x+3))= ((1)/(x+3))^2 + 5((1)/(x+3)) + 6`

To simplify it we take LCD

LCD is (x+3)(x+3)

`(1)/((x+3)(x+3))+5(1*(x+3))/((x+3)(x+3))+(6(x+3)(x+3))/((x+3)(x+3))`

`(1)/(x^2+6x+9)+((5x+15))/(x^2+6x+9)+(6x^2+36x+54)/(x^2+6x+9)`

All the denominators are same so we combine the numerators

`(1+5x+15+6x^2+36x+54)/(x^2+6x+9)`

`(6x^2+41x+70)/(x^2+6x+9)`

Option D is correct