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

1. User Answers harpazo
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.