To determine the domain of the function [tex]\( g(x) = 5 - 2x \)[/tex], we need to consider all the possible values that [tex]\( x \)[/tex] can take such that [tex]\( g(x) \)[/tex] is a defined expression. Let’s go through the steps:
1. Understand the form of the function: [tex]\( g(x) = 5 - 2x \)[/tex] is a linear function, which means it is a polynomial of degree one.
2. Check for undefined expressions: In general, for a function to be defined for some [tex]\( x \)[/tex], we need to ensure that the expression does not lead to undefined values such as division by zero, taking the square root of a negative number, or the logarithm of a non-positive number, among others.
3. Linear functions properties: Linear functions, like [tex]\( g(x) = 5 - 2x \)[/tex], do not have any restrictions based on their form. There are no divisions, square roots, or logarithms involved that could lead to undefined values.
4. Conclusion: Since there are no restrictions or conditions that make the function [tex]\( g(x) \)[/tex] undefined for any real number [tex]\( x \)[/tex], the domain of [tex]\( g \)[/tex] includes all real numbers.
Thus, the domain of the function [tex]\( g(x) = 5 - 2x \)[/tex] is all real numbers.
