Share

# Give Examples of Two Functions F: N → Z And G: Z → Z Such That G O F Is Injective But Gis Not Injective. (Hint: Consider F(X) = X And G(X) =|X|) - CBSE (Commerce) Class 12 - Mathematics

#### Question

Give examples of two functions fN → Z and gZ → Z such that g o f is injective but gis not injective.

(Hint: Consider f(x) = x and g(x) =|x|)

#### Solution

Define fN → Z as f(x) = x and gZ → Z as g(x) =|x|.

We first show that g is not injective.

It can be observed that:

g(−1) = |-1| = 1

g(1) =  |1| = 1

∴ g(−1) = g(1), but −1 ≠ 1.

∴ g is not injective.

Now, gofN → Z is defined as

gof(x) = g(f(x)) = g(x) = |x|

Let xy ∈ N such that gof(x) = gof(y).

⇒ |x| = |y|

Since x and y ∈ N, both are positive.

:. |x| = |y| => x = y

Hence, gof is injective

Is there an error in this question or solution?

#### APPEARS IN

NCERT Solution for Mathematics Textbook for Class 12 (2018 to Current)
Chapter 1: Relations and Functions
Q: 6 | Page no. 29

#### Video TutorialsVIEW ALL [5]

Solution Give Examples of Two Functions F: N → Z And G: Z → Z Such That G O F Is Injective But Gis Not Injective. (Hint: Consider F(X) = X And G(X) =|X|) Concept: Types of Functions.
S