Find the Domain g(x)=-8/(x^2+1)

Problem

g(x)=(−8)/(x2+1)

Solution

1. Identify the type of function. Since g(x) is a rational function, the domain consists of all real numbers except those that make the denominator equal to zero.

2. Set the denominator equal to zero to find potential exclusions.

x2+1=0

3. Solve for x by subtracting 1 from both sides.

x2=−1

4. Analyze the result. Since the square of any real number is non-negative (x2≥0, there is no real number x such that x2=−1

5. Conclude that the denominator is never zero for any real value of x Therefore, the function is defined for all real numbers.

Final Answer

Domain: *(−∞,∞)

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