Question

If f(x) = x² + 5 and g(x) = 5x + 4, what is f o g?

Answer 1

To find the composition f o g, substitute g(x) into f(x), giving us h(x) = 25x² + 40x + 21.

Step-by-step explanation:

The function f o g represents the composition of the functions f and g, meaning we first apply g and then apply f to the result. To compute f o g, we substitute g(x) into f(x):

• First, write down the function g(x) = 5x + 4.
• Next, plug g(x) into f(x), which gives us f(g(x)) = (5x + 4)² + 5.
• Then, expand the square: f(g(x)) = 25x² + 40x + 16 + 5 = 25x² + 40x + 21.

Therefore, the composition f o g is a new function h(x) = 25x² + 40x + 21.