NCERT Solution Class XI Mathematics Relations and Functions Question 8 (Text Sol)

Question 8:

Let f = {(1, 1), (2, 3), (0, −1), (−1, −3)} be a function from Z to Z defined by f(x) = ax + b, for some integers a, b. Determine a, b.

Answer

f = {(1, 1), (2, 3), (0, −1), (−1, −3)}

f(x) = ax + b

(1, 1) ∈ f

⇒f(1) = 1

⇒a × 1 + b = 1

⇒a + b = 1

(0, −1) ∈ f

⇒f(0) = −1

⇒a × 0 + b = −1

⇒b = −1

On substituting b =−1 in a + b = 1, we obtain a + (−1) = 1

⇒ a = 1 + 1 = 2. Thus, the respective values of a and b are 2 and −1.

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