Question

For the functions f(x)=log⁡(x²−2x) and g(x)=x/x−1, which function involves a logarithm?

a) f(x)
b) g(x)
c) Both
d) Neither

Answer 1

The function f(x)=log(x²-2x) involves a logarithm, which is an inverse operation to exponential functions and reflects the property that the log of a division equals the difference of the logs. The answer is a) f(x).

Step-by-step explanation:

The function involving a logarithm between f(x)=log(x²-2x) and g(x)=x/x-1 is f(x). This function features the logarithm of a quadratic expression (x²-2x). Logarithms are operations that are the inverse of exponential functions, which are fundamental in understanding growth patterns and have properties such as the logarithm of the division of two numbers being the difference of their logs. The function g(x), on the other hand, is a rational function, which is a ratio of two polynomials, and does not involve a logarithm.

The function f(x)=log⁡(x²−2x) involves a logarithm.

To determine this, we can look at the equation and see that it has the form log(x). The function g(x)=x/x−1 does not involve a logarithm.

Therefore, the answer is a) f(x).