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Given [tex]\( h(x) = x - 4 \)[/tex],

What is the domain of [tex]\( h \)[/tex]?

Choose one answer:
(A) All real values of [tex]\( x \)[/tex] such that [tex]\( x \neq 4 \)[/tex]
(B) All real values of [tex]\( x \)[/tex] such that [tex]\( x \geq 4 \)[/tex]
(C) All real values of [tex]\( x \)[/tex] such that [tex]\( x \neq 5 \)[/tex]
(D) All real values of [tex]\( x \)[/tex] such that [tex]\( x \geq 5 \)[/tex]
(E) All real values of [tex]\( x \)[/tex]



Answer :

GinnyAnswer
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]

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