Given the parent functions f(x) = log10 x and g(x) = 5x − 2, what is f(x) • g(x)?

f(x) • g(x) = log10 x^5x − 2

f(x) • g(x) = log10 (5x − 2)^x

f(x) • g(x) = 5x log10 x + 2 log10 x

f(x) • g(x) = 2 log10 x − 5x log10 x

### 2 Answers

See the link for an explanation. http://www.mathsisfun.com/sets/functions-compositi…

So if you mean (f º g)(x), then it is f( g(x)), which if you think about it as f(g) = log[10](g), so then f(g(x)) = log[10](5x – 2), and I do not see that as one of your choices.

n log x = log x^n, therefore

f(x) * g(x) = log x^(5x-2)

Learn to use parentheses. They are vital !!!

(And “log” usually IMPLIES a base of 10. It is unnecessary to state it explicitly).