Answer:
f(g(x)) = x^2 +x
Step-by-step explanation:
To find f(g)(x) , we substitute g(x) in for x in the function f(x)
f(x) = x^2 -x
f(g(x)) = g(x)^2 -g(x)
= (x+1)^2 - (x+1)
= (x+1)*(x+1) - (x+1)
FOIL the square
(x+1) (x+1)
First x*x = x^2
outer x*1 = x
inner 1*x = x
last 1*1 =1
Add them together
x^2 + x+x+1 = x^2+2x+1
f(g(x)) = (x+1)*(x+1) - (x+1)
= x^2+2x+1 -(x+1)
Distribute the -1
= x^2 +2x+1 -x-1
= x^2 +x
f(g(x)) is basically replacing the x with g(x).
So, f(x)=(g(x))^2 - g(x)
g(x), in turn, equals x+1
Replace g(x) with x+1
(x+1)^2 - (x+1)
Expand: x^2+x+x+1 - x - 1
Cancel out x and 1
f(g(x))=x^2+x
If you require factoring it's
f(g(x))=x(x+1)
