The relation pairing a real number to its square is a one-to-one function.
Answers
A function for which every element of the range of the function corresponds to exactly one element of the domain is called as a one-to-one function.
Each real number has a unique perfect square. Therefore, the relation is a function.
However, two different real numbers such as 2 and ?2 may have the same square. Therefore, the function is not one-to-one.
Answer:
True
Explanation:
One-to-One Functions
A function f is 1 -to- 1 if no two elements in the domain of f correspond to the same element in the range of f . In other words, each x in the domain has exactly one image in the range. And, no y in the range is the image of more than one x in the domain.
If the graph of a function f is known, it is easy to determine if the function is 1 -to- 1 . Use the Horizontal Line Test. If no horizontal line intersects the graph of the function f in more than one point, then the function is 1 -to- 1 .
A function f has an inverse f−1 (read f inverse) if and only if the function is 1 -to- 1 .
Step-by-step :
An easy way to determine whether a function is a one-to-one function is to use the horizontal line test on the graph of the function. To do this, draw horizontal lines through the graph. If any horizontal line intersects the graph more than once, then the graph does not represent a one-to-one function.
