(a)
To Write:
Write an equation of a relation that contains a radical and its inverse such that the original relation is a function, and its inverse is not a function
(a)
Explanation of Solution
Concept Used:
- A function is :
A relation from a set of inputs to a set of possible outputs where each input is related to exactly one output.
So, for 1 value of x , there should be only 1 value of y .
- A relation is a function if it passes the vertical line test. That is , any vertical line must intersect the graph of the relation at exactly one point for the relation to be function.
- The inverse of a relation is a function , if the graph of the relation passes the horizontal line test.
That is , any horizontal line must intersect the graph of the relation at exactly one point for the inverse of the relation to be a function.
Calculation:
(b)
To Write:
Write an equation of a relation that contains a radical and its inverse such that the original relation is not a function, and its inverse is a function
(b)
Explanation of Solution
Concept Used:
- A function is :
A relation from a set of inputs to a set of possible outputs where each input is related to exactly one output.
So, for 1 value of x , there should be only 1 value of y .
- A relation is a function if it passes the vertical line test. That is , any vertical line must intersect the graph of the relation at exactly one point for the relation to be function.
- The inverse of a relation is a function , if the graph of the relation passes the horizontal line test.
That is , any horizontal line must intersect the graph of the relation at exactly one point for the inverse of the relation to be a function.
Calculation:
Chapter 6 Solutions
Glencoe Algebra 2 Student Edition C2014
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