Find of g(f(x)) when f(x)=sqrt(x+3) and g(x)=(x^2+2)/x.

Question

a. g(f(x))=(x^2+2)(sqrt(x+3))/x
b. g(f(x))=(x+5)/(sqrt(x+3))
c. g(f(x))=(x^2+6x+11)/(sqrt(x+3))
d. g(f(x))=(sqrt(((x^2+2)/x)+3)

Every time I work this problem, I get some crazy answer. Can someone please help me?

Answer 1

g(f) = (f^2+2)/f
= ((√x+3)^2+2)/√(x+3)
= (x+5)/√(x+3)