f(g(x)) means to plug the value of g(x) into every x you see in f(x) and do the math.
g(x) = 3x
f(3x) = 2(3x) - 1
f(3x) = 6x - 1
So, f(g(x)) = 6x - 1.
Understand?
h(f(x)) means to plug the value of f(x) into every x you see in h(x) and do the math.
h(x) = x^2 + 1
h(2x - 1) = (2x - 1)^2 + 1
h(2x - 1) = (2x - 1)(2x - 1) + 1
h(2x - 1) = 4x^2 - 4x + 1 + 1
h(2x - 1) = 4x^2 - 4x + 2
So, h(f(x)) = 4x^2 - 4x + 2
Understand?
This is called COMPOSITION OF FUNCTIONS.
