To determine the domain of the function [tex]\( h(x) = x - 4 \)[/tex], we need to identify all the possible values that [tex]\( x \)[/tex] can take to ensure the function is defined.
1. Understanding the function [tex]\( h(x) \)[/tex]:
- The function [tex]\( h(x) = x - 4 \)[/tex] is defined for all real numbers.
- This expression can be evaluated for any real number without encountering undefined operations or restrictions (e.g., division by zero, square root of a negative number, etc.).
2. Identify any restrictions:
- Since the function [tex]\( h(x) = x - 4 \)[/tex] involves only basic arithmetic (subtraction of 4 from [tex]\( x \)[/tex]), and subtraction is always defined for real numbers, there are no restrictions on the values that [tex]\( x \)[/tex] can take.
3. Conclusion:
- Because there are no values of [tex]\( x \)[/tex] that would make the function [tex]\( h(x) \)[/tex] undefined, the domain of [tex]\( h \)[/tex] is all real numbers.
Therefore, the domain of the function [tex]\( h(x) = x - 4 \)[/tex] is all real numbers. The correct answer is:
(E) All real values of [tex]\( x \)[/tex]
