How to solve this problem

Question

f(x) = 2x + 7 and g(x) = 9x - 1

what is f(g(x))?

Answer 1

f(g(x)) is f of g of x. Generally, you want to plug the INSIDE function into the OUTSIDE function. So since the inside function is g(x) = 9x-1, this implies that f(g(x)) = f(9x-1). So we plug this into the outside, namely f(x)= 2x+7. Wherever you see an x, this will now become 9x - 1. So f(9x-1) = 2(9x-1) + 7. We can clean this up using the distributive method and combining like terms. So 2(9x-1) + 7 = (18x - 2) + 7 = 18x + 5. Thus f(g(x)) = 18x + 5