Question

Let f (x) = 2x - 1, g(x) = 3x, and h(x) = x2 + 1. Compute the following: f (g (x)) and h (f (x))

Answer 1

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.