Question

Let f = {(–1, 3), (0, –1), (2, –9)} be a linear function from Z into Z. Find f(x)

Answer 1

The linear equation is f(x) = ax + b

f(– 1) = 3

a(– 1) + b = 3

–a + b = 3 ….(1)

f(0) = – 1

a(0) + b = – 1

0 + b = – 1

b = – 1

Substitute the value of b = – 1 in (1)

–a – 1 = 3

–a = 3 + 1

–a = 4

a = – 4

∴ The linear equation is – 4(x) – 1 = – 4x – 1 or – (4x + 1)