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

Question

imstuck · Answer

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.