Given the parent functions f(x) = log10 x and g(x) = 3x − 1, what is f(x) • g(x)?

f(x) • g(x) = log10 (3x − 1)x
f(x) • g(x) = log10 x3x − 1
f(x) • g(x) = 3x log10 x + log10 x
f(x) • g(x) = log10 x − 3x log10 x

Question

Given the parent functions f(x) = log10 x and g(x) = 3x − 1, what is f(x) • g(x)?

 f(x) • g(x) = log10 (3x − 1)x
 f(x) • g(x) = log10 x3x − 1
 f(x) • g(x) = 3x log10 x + log10 x
 f(x) • g(x) = log10 x − 3x log10 x

mathmale · Answer

this is straightforward multiiplication.  f(x) multiplies g(x) and results in 

f(x)*g(x), on the left side.  On the right side, (log to the base 10 of x)*(3x-1).  You need not do any more; this function can't be simplified.

mikwind · Answer

I don't think this is multiplication, it is a compound operator, as in f(x)$$f(x)*g(x) = f(g(x))$$

mikwind · Answer

but that would be $$f(g(x))=\log_{10} (3x-1)$$ which isn't in the answers