Question

If f(x) = x2 + 5 and g(x) = 5x + 4, what is [f o g]?
a) 34 209
b) 1,161
c) 1,394

Answer 1

To find the composite function [f o g], substitute the function g(x) into the function f(x). The composite function [f o g] is 25x^2 + 40x + 29.

Step-by-step explanation:

To find the composite function [f o g], we substitute the function g(x) into the function f(x).

First substitute g(x) into f(x): f(g(x)) = (g(x))^2 + 5.

Since g(x) = 5x + 4, we can replace g(x) in the equation: f(g(x)) = (5x + 4)^2 + 5.

Expanding and simplifying, we get: f(g(x)) = 25x^2 + 40x + 24 + 5 = 25x^2 + 40x + 29.

So the composite function [f o g] is 25x^2 + 40x + 29.