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

Solution:

A function is a process or a relation that associates each element 'a' of a non-empty set A, to a single element 'b' of another non-empty set B. A relation f from a set A (the domain of the function) to another set B (the co-domain of the function) is called a function in math.

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

Also, f, g : A → B is defined by x² - x , x ∈ A and g (x)

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 = 0

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

⇒ f (1) = g (1)

f (2) = (2)² - 2 = 2

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

⇒ f (2) = g (2)

Therefore,

f (a) = g (a) ∀a ∈ A

Hence, the functions f and g are equal

NCERT Solutions for Class 12 Maths - Chapter 1 Exercise ME Question 15