Answer:
option D
Step-by-step explanation:
[tex]f(x) = x^2 + 5x + 6[/tex]
[tex]g(x)= \frac{1}{x+3}[/tex]
(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)
[tex]f(g(x))= f(\frac{1}{x+3})= (\frac{1}{x+3})^2 + 5(\frac{1}{x+3}) + 6[/tex]
To simplify it we take LCD
LCD is (x+3)(x+3)
[tex]\frac{1}{(x+3)(x+3)}+5\frac{1*(x+3)}{(x+3)(x+3)}+\frac{6(x+3)(x+3)}{(x+3)(x+3)}[/tex]
[tex]\frac{1}{x^2+6x+9}+\frac{(5x+15)}{x^2+6x+9}+\frac{6x^2+36x+54}{x^2+6x+9}[/tex]
All the denominators are same so we combine the numerators
[tex]\frac{1+5x+15+6x^2+36x+54}{x^2+6x+9}[/tex]
[tex]\frac{6x^2+41x+70}{x^2+6x+9}[/tex]
Option D is correct
