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

We know that
f(x) = 3x - 3 and g(x) = x^2 - 2. We need fog(x) and gof(x)

fog(x) =
f(g(x))

=> f(x^2 - 2)

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

=> 2x^2 - 4 - 3

=> 2x^2 - 7

gof(x) =
g(f(x))

=> g( 2x - 3)

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

=> 4x^2 + 9 - 12x - 2

=> 4x^2 - 12x + 7

This gives fog(x) = 2x^2 - 7 and gof(x) = 4x^2 - 12x +
7