If f(x) = 2x-3 and g(x) = x^2 -2 find fog(x) and gof(x).

f(x) = 2x-3

g(x) = x^2
-2

We need to find fog(x) and
gof(x).

We know that fog(x) =
f(g(x))

Then we will substitute with g(x) = x^2
-2

==> fog(x) = f( x^2 -2)

Now
we will substitute with x = x^2-x in f(x).

==> fog(x) =
2(x^2-2) -3

We will open
brackets.

==> fog(x) = 2x^2 -4
-3

==> fog(x) = 2x^2 -7

gof(x) =
g(f(x)) = g(2x-3) = (2x-3)^2 -2 = 4x^2 -12x + 9 -2 = 4x^2 -12x
+7

==> fog(x) = 2x^2 -7

==> gof(x) = 4x^2 -12x +
7