Question

Let f(x) = log(x² - 2x) and g(x) = x / (x - 1). Find the expression for (f * g)(x).

a. log(x² - 2x) / (x - 1)
b. x² / (x² - 2x - x + 1)
c. x² / (x² - 2x)
d. log(x² - 2x) * (x - 1)

Answer 1

To find the composite function (f * g)(x) with f(x) = log(x² - 2x) and g(x) = x / (x - 1), we substitute g(x) into f(x). However, the resulting expression does not match any of the provided options, suggesting an error in the question or answer choices.

Step-by-step explanation:

The student has asked to find the expression for the composite function (f * g)(x), where f(x) = log(x² - 2x) and g(x) = x / (x - 1). Applying the definition of function composition, we get:

(f * g)(x) = f(g(x)) = f(x / (x - 1)).

To evaluate this, we replace every occurrence of x in f(x) with g(x):

(f * g)(x) = log((x / (x - 1))² - 2*(x / (x - 1))).

However, none of the provided answer choices match this expression. It seems there might have been an error in the question's phrasing or the given answer choices. Therefore, more context or clarification is needed to provide a correct response.