NCERT Class XI Mathematics - Relations and Functions - Solutions
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Question : 32
Total: 36
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.
Solution:
Given f(x) = ax + b, for some integers a, b.
When (1, 1) ∈ f ⇒ f (1) = a + b = 1
⇒ a + b = 1 ...(i)
When (2, 3) ∈ f ⇒ f (2) = 2a + b = 3
⇒ 2a + b = 3 ...(ii)
Subtract (i) from (ii), we get a = 2
Put a = 2 in (i), we get b = – 1.
Hence a = 2, b = – 1.
When (1, 1) ∈ f ⇒ f (1) = a + b = 1
⇒ a + b = 1 ...(i)
When (2, 3) ∈ f ⇒ f (2) = 2a + b = 3
⇒ 2a + b = 3 ...(ii)
Subtract (i) from (ii), we get a = 2
Put a = 2 in (i), we get b = – 1.
Hence a = 2, b = – 1.
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