Given f(x) = 2x + 3 and g(x) = x^2 - 1, find (f ∘ g)(x).

Step 1: Recall the meaning of function composition.

The notation (f ∘ g)(x) means:
f(g(x))

This tells us to apply g first and then use its output as the input of f.

Step 2: Write the two functions.

f(x) = 2x + 3
g(x) = x^2 - 1

Step 3: Substitute g(x) into f.

Since f(x) = 2x + 3, replace x in f with x^2 - 1:

f(g(x)) = 2(x^2 - 1) + 3

Step 4: Distribute the 2.

f(g(x)) = 2x^2 - 2 + 3

Step 5: Combine like terms.

f(g(x)) = 2x^2 + 1

Therefore:
(f ∘ g)(x) = 2x^2 + 1.