Q. 5 C3.8( 18 Votes )

# State with reason whether following functions have inverseh: {2, 3, 4, 5} → {7, 9, 11, 13} withh = {(2, 7), (3, 9), (4, 11), (5, 13)}

It is given that h: {2, 3, 4, 5} {7, 9, 11, 13} with

h = {(2, 7), (3, 9), (4, 11), (5, 13)}

We can see that all distinct elements of the set (2, 3, 4, 5) have distinct images under h.

h is one–one.

Also, h is onto since for every element of the set {7, 9, 11, 13},

there exists an element x in the set {2, 3, 4, 5} such that h(x) = y.

Therefore, h is a one–one and onto function.

Therefore, h has an inverse.

Rate this question :

How useful is this solution?
We strive to provide quality solutions. Please rate us to serve you better.
Related Videos
Functions - 0152 mins
Different kind of mappings58 mins
Range of Functions58 mins
Quick Revision of Types of Relations59 mins
Some standard real functions61 mins
Battle of Graphs | various functions & their Graphs48 mins
Functions - 0947 mins
Quick Recap lecture of important graphs & functions58 mins