Find the Domain and Range f(x)=1/x

Problem

ƒ(x)=1/x

Solution

1. Identify the domain by finding all values of x for which the function is defined. Since division by zero is undefined, the denominator x cannot be zero.

x≠0

2. Express the domain in interval notation. The domain includes all real numbers except zero.

Domain: *(−∞,0)∪(0,∞)

3. Identify the range by determining the possible values of ƒ(x) or y Set the equation to y and solve for x

y=1/x

4. Rearrange the equation to isolate x

x=1/y

5. Determine restrictions on y Similar to the domain, the denominator y cannot be zero. As x approaches infinity, y approaches zero but never reaches it.

y≠0

6. Express the range in interval notation. The range includes all real numbers except zero.

Range: *(−∞,0)∪(0,∞)

Final Answer

Domain: *(−∞,0)∪(0,∞), Range: *(−∞,0)∪(0,∞)

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