Question

Let f(x) = x2 + x + 3 and g(x) = x + 5. Find f(g(x)). Show each step of your work. PLEASE HELP ME :-( I will appreciate it because I feel very sick and i just need to know how to do this so my homework is done and i could go lay down.

Answer 1

f(g(x)) means you have to substitute g(x) equation into x in f(x) equation, so:

$f(x+5) = (x+5)^2+(x+5)+3\\\\f(x+5) = x^2 + 10x + 25 + x + 5 + 3\\\\f(x+5) = x^2 + 11x + 33$

Therefore, f(g(x)) = x^2 + 11x + 33