Calculus Homework Question

Question

Provided f(x) = √ x + 2 and g(x) = x / x + 1 , find (f ◦ g)(3) and (g ◦ f)(3).

Answer 1

Function composition

#1 ) (f*g)(3) --> sqrt(x/(x+1)) + 2 | x=3 --> sqrt(3/4) + 2 -> sqrt(3)/2 + 4/2 --> (4 + sqrt(3))/2

#2 ) (g*f)(3) --> (sqrt(x) + 2) /( sqrt(x) + 2 + 1) | x=3 --> (sqrt(3) + 2)/(sqrt(3) + 3)