Question

Function s is the set of points: {(4,3),(5,3),(8,6),(9,6),(12,9),(13,9)}

Answer 1

Given:

The function in the form of set of points is

$s:\{(4,3),(5,3),(8,6),(9,6),(12,9),(13,9)\}$

To find:

(a) The inverse of function s.

(b) whether the inverse of function s is a function?

Solution:

(a)

If a function is $f:\{(a,b),a,b\in R\}$, then its inverse function is

$f^{-1}:\{(b,a),a,b\in R\}$

We have,

$s:\{(4,3),(5,3),(8,6),(9,6),(12,9),(13,9)\}$

So, inverse of this function is

$s^{-1}:\{(3,4),(3,5),(6,8),(6,9),(9,12),(9,13)\}$

Therefore, the inverse of function s is $s^{-1}:\{(3,4),(3,5),(6,8),(6,9),(9,12),(9,13)\}$.

(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.