Question

Given the parent functions f(x) = log2 (3x − 9) and g(x) = log2 (x − 3), what is f(x) − g(x)?. A. f(x) − g(x) = log2 (2x − 6). B. f(x) − g(x) = log2 (2x − 12). C. f(x) − g(x) = log2 one third. D. f(x) − g(x) = log2 3

Answer 1

We are given the two functions:
f(x) = log2 (3x − 9)
g(x) = log2 (x − 3)

Then,
f(x) - g(x) = log2 (3x - 9) - log2 (x - 6) 

Two logarithms of the same bases are subtracted, therefore:
log2 ((3x - 9) / (x - 3))

We factor both the numerator and the denominator by x - 3. This becomes,
log2 ((3)(x - 3) / (x - 3)) 

When further simplified, yields:
log2 (3)

Answer 2

F(x) - g(x) = log2 (3x - 9) - log2 (x - 6) 

When two logarithms of the same bases are subtracted they become,
                               log2 ((3x - 9) / (x - 3))
Both the numerator and the denominator can be factored by x - 3. This becomes,
                               log2 ((3)(x - 3) / (x - 3)) 
which simplifies into,
                                      log2 (3).