Find the Domain 200/(2+x^2)

Problem

200/(2+x2)

Solution

1. Identify the potential restrictions for the domain of a rational function. The denominator of a fraction cannot be equal to zero.

2. Set the denominator equal to zero to find any excluded values:

2+x2=0

3. Solve for x by subtracting 2 from both sides:

x2=−2

4. Analyze the result. Since the square of any real number x is always non-negative (x2≥0, there is no real value of x that satisfies x2=−2

5. Conclude that because the denominator 2+x2 is always greater than or equal to 2, it will never be zero for any real number x Therefore, the domain is all real numbers.

Final Answer

Domain: *(−∞,∞)

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