Let f = {1,1),(2,3)(0,-1),(-1-3}} be a linear function from Z into Z.

1.	Let f = {1,1),(2,3)(0,-1),(-1-3}} be a linear function from Z into Z. Find f (x).
Answer» Let the function be f (x) = ax + b f(1) = a(1) + b = a + b = 1 ⇒ f(2) = a(2) + b = 2a + b = 2 f(0) = a(0) + b = [b = -1] …..(1) f(-1) = a(-1) + b = -3 ∴ b – a = -3 … (2) (i) in (2) (-1) -a = -3 ∴ -1 + 3 = a ∴ a = 2 ∴ f(x) = 2x – 1.

Let f = {1,1),(2,3)(0,-1),(-1-3}} be a linear function from Z into Z. Find f (x).

Answer»

Let the function be f (x) = ax + b

f(1) = a(1) + b = a + b = 1

⇒ f(2) = a(2) + b = 2a + b = 2 f(0) = a(0) + b = [b = -1] …..(1)

f(-1) = a(-1) + b = -3

∴ b – a = -3 … (2)

(i) in (2) (-1) -a = -3

∴ -1 + 3 = a

∴ a = 2

∴ f(x) = 2x – 1.

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Let f = {1,1),(2,3)(0,-1),(-1-3}} be a linear function from Z into Z. Find f (x).

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