Final answer:
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.