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Given the function [tex]g(x) = 5 - 2x[/tex], what is the domain of [tex]g[/tex]?

Sagot :

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.
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