Given:
The function in the form of set of points is
[tex]s:\{(4,3),(5,3),(8,6),(9,6),(12,9),(13,9)\}[/tex]
To find:
(a) The inverse of function s.
(b) whether the inverse of function s is a function?
Solution:
(a)
If a function is [tex]f:\{(a,b),a,b\in R\}[/tex], then its inverse function is
[tex]f^{-1}:\{(b,a),a,b\in R\}[/tex]
We have,
[tex]s:\{(4,3),(5,3),(8,6),(9,6),(12,9),(13,9)\}[/tex]
So, inverse of this function is
[tex]s^{-1}:\{(3,4),(3,5),(6,8),(6,9),(9,12),(9,13)\}[/tex]
Therefore, the inverse of function s is [tex]s^{-1}:\{(3,4),(3,5),(6,8),(6,9),(9,12),(9,13)\}[/tex].
(b)
A set of point is a function if there exist unique output for each input.
In inverse of s, we have two output values y=4 and y=5 for single input x=3.
Therefore, the inverse of function s is not a function.
