Question

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

A. (g*f)(x)=x+4/sqrt x+1

B. (g*f)(x)=x^2+2x+4/sqrt x+1

C. (g*f)(x)= (x^2+3)(sqrt x+1)/x

D. (g*f)(x)=sqrt x^2+3/x +1

I think its A or B...I'm not sure.

Answer 1

You will have to be sure.

Here is a method you can follow and you will always get it right:

(g•f)(x) = g(f(x))
now f(x) = √x+1 , so replace it is g(f(x))
g(√x + 1) , now note that g(x) = x^2+3/x , so we have to replace the x with x^2+3/x

g(f(x)) = (√x + 1)^2 + 3/(√x + 1)
which does not simplify to any of the choices, so ....

I think you left out some brackets, and it could have been
f(x) = √(x+1)
if so ...
g(f(x))
= g(√(x+1) )
= √(x+1)^2 + 3/√(x+1)
= x+1 + 3/√(x+1)

not a choice either
was it g(x) = (x^2+3)/x , I will not keep guessing

check your typing and repost.

can you see how important these brackets are ?