Concept explainers
True or False? Justify your answer with a proof or a counterexample.
310. A function is always one-to-one.
To calculate: Justify the statement with a proof or a counterexample
“A function is always one-to-one.”
Answer to Problem 310RE
The statement “A function is always one-to-one” is false.
Explanation of Solution
Given information: Given statement is “A function is always one-to-one.”
Formula used: A function is said to be one-to-one, if every element of the range of the function corresponds to exactly one element of the domain.
For a function to be one-to one
If
Then
Calculation:
Let us consider an example.
Let
This implies that
Thus, for element in range, there exists two elements in domain.
Hence, the function is not always one-to-one.
Conclusion:
Hence, the statement “A function is always one-to-one” is false.
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