Question

if f:Z-Z is a linear function, defined by f={(1,1),(0,-1),(2,3)},find f(x)​

Answer 1

The linear function is of the form:

$\bold{f(x) = 2x -1}$

Step-by-step explanation:

We are given the following in the question:

A function f is defined by:

$f(x)=\{(1,1),(0,-1),(2,3)\}$

Since f(x) is a linear function, we can write,

$f(x) = ax + b$

Putting the values, we get the equations:

$f(1) = 1\\a(1) + b = 1\\a+b =1\\f(0) = -1\\a(0) + b = -1\\\Rightarrow b = -1\\f(2) = 3\\a(2) +b = 3\\2a + b = 3\\\text{Solving we get}\\a = 1 + 1 = 2$

Thus, the linear function is of the form:

$f(x) = 2x -1$

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