Question

What is the domain for the exponential function f (x) = –5log(x – 2)?

Answer 1

The domain of the function f(x) = -5log(x - 2) is (2, infinity), meaning that x must be greater than 2 for the function to have real values.

Step-by-step explanation:

The domain for the function f(x) = –5log(x – 2) relates to the set of all possible values of x that can be plugged into the function without resulting in any undefined or non-real values. Since the logarithmic function is defined only for positive real numbers, the argument (x – 2) must be greater than 0. This means x must be greater than 2. Therefore, the domain of f(x) is (2, ∞).

Answer 2

The domain for the exponential function f(x) is (2, ∞) or x.

In Mathematics and Euclidean Geometry, a domain is the set of all real numbers (x-values) for which a particular relation or function is defined.

Generally speaking, the domain of any logarithmic function is from (x > 0) to infinity (+∞). Thus, its graph moves to the right on the vertical axis and it increases to infinity (+∞) as the value of x increases.

For the restriction on the domain of this function, we have;

x - 2 ≠ 0

x ≠ 2

In this context, we can logically deduce the following domain:

Domain = (2, ∞) or x > 2.