To determine the domain of the function [tex]\( y = 1 - \log_{10} x \)[/tex], we need to identify the values of [tex]\( x \)[/tex] for which the expression is defined.
1. Understanding the Logarithm Function:
The logarithm function [tex]\(\log_{10} x\)[/tex] is defined only for positive values of [tex]\( x \)[/tex]. This is because the logarithm of a non-positive number (zero or a negative number) is undefined in the real number system. Hence, for [tex]\(\log_{10} x\)[/tex] to be defined:
[tex]\[
x > 0
\][/tex]
2. Function Analysis:
- We start with the function [tex]\( y = 1 - \log_{10} x \)[/tex].
- The term [tex]\(\log_{10} x\)[/tex] requires [tex]\( x \)[/tex] to be strictly greater than 0.
3. Conclusion:
Combining the above observations, we conclude that [tex]\( x \)[/tex] must be greater than 0 for the function [tex]\( y = 1 - \log_{10} x \)[/tex] to be defined.
Therefore, the domain of the function [tex]\( y = 1 - \log_{10} x \)[/tex] is:
[tex]\[
(0, \infty)
\][/tex]
