Question

Let f(x)=x+3 and g(x)=1/x. The graph of (f*g)(x) is shown below.

Answer 1

For this case we have the following functions:
 $f (x) = x + 3 g (x) = 1 / x$ When composing the functions we have:
 $(fog) (x) = f (g (x))$
 Substituting values we have:
 $(fog) (x) = ((1 / x) +3)$
 Rewriting:
 $(fog) (x) = 1 / x + 3$
 The function has a horizontal asymptote at y = 3.
 Therefore, the range of the function is all reals minus y = 3.
 Answer:
 option 3