Let f = {(0, -5), (1, -2), (3, 4), (4, 7)} be a linear function from Z

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

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

Answer»

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