Let f (x) = –5x + 3 and g(x) = 6x – 2. Find f • g and its domain.

Answer 1

To find f • g, we need to substitute g(x) into f(x). So we have:

f • g(x) = f(g(x)) = f(6x - 2)

Now, substitute f(x) into the expression above:

f(6x - 2) = -5(6x - 2) + 3 = -30x + 10 + 3 = -30x + 13

The domain of f • g is the same as the domain of g(x), which is all real numbers because there are no restrictions on x in the expression 6x - 2.

Therefore, the domain of f • g is (-∞, +∞).