Find the Domain g(x)=|x|-7

Problem

g(x)=|x|−7

Solution

1. Identify the type of function. The function g(x)=|x|−7 is an absolute value function.

2. Analyze the expression for any restrictions. A function's domain is restricted if there are denominators that could be zero, square roots of negative numbers, or logarithms of non-positive numbers.

3. Determine if any such restrictions exist here. Since the absolute value of any real number x is defined and there are no divisions or roots, x can be any real number.

4. Express the domain in interval notation. Since there are no restrictions, the domain includes all values from negative infinity to positive infinity.

Final Answer

Domain: *(−∞,∞)

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