Question

If f(x) = x^2-x and g(x) = x-1 what is f(g(x))?

Answer 1

This is a composite function. You need to apply g(x) to f(x) in a combination. If g(x) = x - 1, f(g(x)) means that you have to fill the g(x) value into the f(x) wherever you see an x. Here's how that works. G(x) = x - 1. F(x) = x^2 - x. Fill "x - 1" in for those x's.\[f(x)=x ^{2}-x-->(x-1)^{2}-(x-1)\]Now expand this by FOILING out the first term. Now combine those like terms to get\[f(g(x))=x ^{2}-3x+2\]This can also be factored and solved.\[x ^{2}-3x+2=(x-2)(x-1)\]So the solutions, if you need them, of the composition of f(x) and g(x) in f(g(x)) is x = 2 and x = 1. Sorry this explanation was so so long.