Question

Find (f ∙ g)(2) when f(x) = and g(x) = x + 9.

Answer 1

Answer: We can start by evaluating g(2):

g(2) = 2 + 9 = 11

Now we can use the definition of function composition to evaluate (f ∙ g)(2):

(f ∙ g)(2) = f(g(2)) = f(11)

To find f(11), we need to substitute 11 for x in the expression for f(x):

f(11) = (11 - 3)^2 + 1 = 8^2 + 1 = 65

Therefore, (f ∙ g)(2) = f(g(2)) = f(11) = 65.

Explanation: