In Problems 13-20, determine whether the function is one-to-one.
In Problems 13-20, determine whether the function is one-to-one.
Solution Summary: The author explains that a function is not one-to-one if two different inputs in the domain correspond to the same output of the range.
In Problems 13-20, determine whether the function is one-to-one.
Expert Solution & Answer
To determine
To find: Determine whether the function is one-to-one.
Answer to Problem 14AYU
Solution:
No, the given function is not one – to – one function.
Explanation of Solution
Given:
Calculation:
A function is one-to-one if any two different inputs in the domain correspond to two different outputs in the range. That is, if and are two different inputs of a function , then is one-to-one if .
In other way, a function is one-to-one if no in the range is the image of more than one in the domain. A function is not one-to-one if any two (or more) different elements in the domain correspond to the same element in the range.
In the domain, we have 4 different inputs and also in the range, 3 different outputs, if we map the function, we should get different values as given in the data.
But two inputs of the domain have the same output of the range. That is, the names John and Chuck have the same Phoebe as its range. As the consequence, the given function is not one-to-one, because two different elements in the domain correspond to the same element in the range.
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