Question

What is the domain of ​f(x)equalsStartFraction 1 Over x EndFraction
​? What is its​ range?
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Part 1
The domain of ​f(x)equalsStartFraction 1 Over x EndFraction
is
  
left parenthesis negative infinity,0 right parenthesis union left parenthesis 0,infinity right parenthesis.
​(Type your answer in interval​ notation.)
Part 2
The range of ​f(x)equalsStartFraction 1 Over x EndFraction
is
  
left parenthesis negative infinity,0 right parenthesis.

Answer 1

Part 1 — Domain: (-∞, 0) ∪ (0, ∞).
Reason: x cannot be 0 because 1/0 is undefined.

Part 2 — Range: (-∞, 0) ∪ (0, ∞).
Reason: 1/x can never equal 0, so 0 is not in the range. For any nonzero y, take x = 1/y and then f(x) = 1/(1/y) = y, so every nonzero real value is attained.