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# State with Reason Whether Following Functions Have Inverse H: {2, 3, 4, 5} → {7, 9, 11, 13} With H = {(2, 7), (3, 9), (4, 11), (5, 13)} - CBSE (Science) Class 12 - Mathematics

ConceptComposition of Functions and Invertible Function

#### Question

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

#### Solution

h: {2, 3, 4, 5} → {7, 9, 11, 13} defined as:

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

It is seen that all distinct elements of the set {2, 3, 4, 5} have distinct images under h.

∴Function h is one-one.

Also, h is onto since for every element y of the set {7, 9, 11, 13}, there exists an element x in the set {2, 3, 4, 5}such that h(x) = y.

Thus, h is a one-one and onto function. Hence, h has an inverse.

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#### APPEARS IN

NCERT Solution for Mathematics Textbook for Class 12 (2018 to Current)
Chapter 1: Relations and Functions
Q: 5.3 | Page no. 18

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Solution State with Reason Whether Following Functions Have Inverse H: {2, 3, 4, 5} → {7, 9, 11, 13} With H = {(2, 7), (3, 9), (4, 11), (5, 13)} Concept: Composition of Functions and Invertible Function.
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