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# Let a = {−1, 0, 1, 2}, B = {−4, −2, 0, 2} and F, G: a → B Be Functions Defined by F(X) = X2 − X, X ∈ a Justify Your Answer. (Hint: One May Note that Two Function F: a → B and G: a → B Such that F(A) = G(A) andMnfore;A ∈A, Are Called Equal Functions). - CBSE (Commerce) Class 12 - Mathematics

#### Question

Let A = {−1, 0, 1, 2}, B = {−4, −2, 0, 2} and fgA → B be functions defined by f(x) = x2 − xx ∈ A and g(x) = 2|x - 1/2|- 1, x in A. Are f and g equal?

Justify your answer. (Hint: One may note that two function fA → B and g: A → B such that f(a) = g(a) &mn For E;a ∈A, are called equal functions).

#### Solution

It is given that A = {−1, 0, 1, 2}, B = {−4, −2, 0, 2}.

Also, it is given that fgA → B are defined by f(x) = x2 − xx ∈ A and g(x) = 2|x - 1/2| - 1, x in A.

It is observed that:

f(-1) = (1^2) - (-1) = 1+1 = 2

g(-1) = 2|(-1)-1/2| - 1= 2(3/2) - 1= 3 -1  =2

=> f(-1) = g(-1)

f(0) = (0)^2 - 0 = 0

g(0) = 2|0 - 1/2| -  1 = 2(1/2) - 1= 1 - 1 = 0

=> f(0) = g(0)

f(1) = (1)^2 - 1 = 1 -   1 = 0

g(1) = 2|a - 1/2| - 1= 2(1/2) - 1= 1 -1 = 0

=>f(1) = g(1)

f(2) = (2)^2 - 2 = 4 - 2 = 2

g(2) = 2|2-1/2| - 1 = 2(3/2)-1 = 3 -1 = 2

=> f(2) = g(2)

:. f(a) = g(a) ∀ a ∈ A

Hence, the functions and g are equal.

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: 15 | Page no. 30

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Solution Let a = {−1, 0, 1, 2}, B = {−4, −2, 0, 2} and F, G: a → B Be Functions Defined by F(X) = X2 − X, X ∈ a Justify Your Answer. (Hint: One May Note that Two Function F: a → B and G: a → B Such that F(A) = G(A) andMnfore;A ∈A, Are Called Equal Functions). Concept: Types of Functions.
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