Functions-13

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Let f = {(1,1), (2,3), (0,-1), (-1,-3)} be a function described by the formula f(x) = ax + b for some integers a, b.
Determine a, b.

Solution: We have. f(1) = 1, f(2) = 3, f(0) = -1 and f(-1) = -3.

It is given that f(x) = ax + b. Therefore,

f(1) = 1 and f(2) = 3 => a + b = 1 and 2a + b = 3 => a = 2, b = -1.

Thus, f(x) = 2x - 1. Clearly, f(0) = -1 and f(-1) = -3 are true.

Hence, a = 2 and b = -1.

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