If f(x)=-x^2 and g(x) =x+1 find (fog)(x) and (gof)(x)
f(g(x))= -(x+1)^2
g(f(x))= (-x^2 + 1)
To find (fog)(x), we need to substitute g(x) into f(x).
First, let's find g(f(x)):
g(f(x)) = g(-x^2)
Now substitute the expression for g(x):
g(f(x)) = -x^2 + 1
Therefore, (fog)(x) = -x^2 + 1.
To find (gof)(x), we need to substitute f(x) into g(x).
First, let's find f(g(x)):
f(g(x)) = f(x + 1)
Now substitute the expression for f(x):
f(g(x)) = -(x + 1)^2
Therefore, (gof)(x) = -(x + 1)^2.
So, to summarize:
(fog)(x) = -x^2 + 1
(gof)(x) = -(x + 1)^2