Question

Let A = {−1, 0, 1, 2}, B = {−4, −2, 0, 2} and f, g: A → B be functions defined by f(x) = x 2 − x, x ∈ A and. Are f and g equal? Justify your answer. (Hint: One may note that two function f: A → B and g: A → B such that f(a) = g(a) "a ∈A, are called equal functions).

Answer 1

question is ----> 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 and $g(x)=2|x-1/2|-1$, x ∈ A. Are f and g equal?

solution :- $\bf{concept}$ two functions f: A → B and g: A → B such that f (a) = g(a) ∀ a ∈ A, are called equal functions.

Let's check :
A = {-1, 0 , 1 , 2}
take x = -1
f(-1) = (-1)² - (-1) = 1 + 1 = 2
g(-1) = 2|-1- 1/2| - 1 = 2 × 3/2 - 1 = 3 - 1 = 2
hence, f(-1) = g(-1) = 2

take x = 0
f(0) = 0² - 0 = 0
g(0) = 2|0 - 1/2| - 1 = 1 × 1/2 - 1 = 1 - 1 = 0
hence, f(0) = g(0) = 0

take , x = 1
f(1) = 1² - 1 = 1 - 1 = 0
g(1) = 2|1 - 1/2| - 1 = 2 × 1/2 - 1 = 0
hence, f(1) = g(1) = 0

take , x = 2
f(2) = 2² - 2 = 4 - 2 = 2
g(2) = 2|2 - 1/2| -1 = 2 × 3/2 - 1 = 2
hence, f(2) = g(2) = 2

here we can see that f(a) = g(a) ∀ a ∈ A
hence, f and g are equal functions.

Answer 2

Answer:

...............☝☝☝☝☝..