Question

please say this answer

Answer 1

Given that f(x) is a linear function.

Let f(x) = ax + b

We are given 4 points:
f(1) = 1
f(2) = 3
f(0) = -1
f(-1) = -3

Since we have two unknowns(a and b), we need two equations to find them.

f(0) = -1
=> a×0 + b = -1
=> b = -1

f(1) = 1
=> a×1 + (-1) = 1
=> a - 1 = 1
=> a = 1+1 =2

Thus f(x) = 2x - 1

Check the rest two points if it satisfies or not:
f(2) = 2×2 -1 = 4 -1 = 3 (satisfied)
f(-1) = 2×(-1) - 1 = -2 - 1 = -3 (satisfied)

Thus f(x) = 2x - 1