Question

Let f = {(0, -5), (1, -2), (3, 4), (4, 7)} be a linear function from Z into Z. Write an expression for f.

Answer 1

Given that: f = {(0, -5), (1, -2), (3, 4), (4, 7)} be a function from Z to Z defined by linear function. 

We know that, linear functions are of the form y = mx + b 

Let f(x) = ax + b, for some integers a, b 

Here, (0, -5) ∈ f 

⇒ f(0) = -5 

⇒ a(0) + b = -5 

⇒ b = -5 …(i) 

Similarly, (1, -2) ∈ f 

⇒ f(1) = -2 

⇒ a(1) + b = -2 

⇒ a + b = -2 

⇒ a + (-5) = -2 [from (i)] 

⇒ a = -2 + 5

⇒ a = 3 

∴ f(x) = ax + b 

= 3x + (-5) 

f(x) = 3x – 5