If f(x)=2x-1 and g(x)=x^2-x find :
1. g(g(x))
2. g(f(x))
3. f(g(x))
4. f(f(x))
just substitute and evaluate
g(x) = x^2-x, so
g(g) = g^2-g = (x^2-x)^2 - (x^2-x)
g(f) = f^2-f = (2x-1)^2 - (2x-1)
f(x) = 2x-1, so
f(g) = 2g-1 = 2(x^2-x)-1
f(f) = 2f-1 = 2(2x-1)-1
expand those out if you desire.