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

Solution:

It is given that the two parent functions are: 

f(x) = log10 x

g(x) = 5x - 2

We have to find f(x).g(x)

f(x).g(x) = log10x.(5x - 2)

By further calculation

= log10x (5x) + log10 x (-2)

So we get

= 5x log10 x - 2 log 10 x

Therefore, f(x).g(x) = 5x log10 x - 2 log 10 x.

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

Summary:

Given the parent functions f(x) = log10 x and g(x) = 5x - 2, f(x).g(x) is 5x log10 x - 2 log 10 x.