Question

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

Answer 1

Answer:

f(x) = -4x - 1

Solution:

• Given : f = {(-1,3) , (0,-1) , (2,-9)}
• To find : f(x) = ?

It is given that the given function is linear .

Also,

The general form of a linear function is given as ; y = f(x) = ax + b .

Thus let the given function be ;

y = f(x) = ax + b

★ For (-1,3) , x = -1 and y = 3

Thus,

=> y = ax + b

=> 3 = a•(-1) + b

=> 3 = -a + b

=> a = b - 3 --------(1)

★ For (0,-1) , x = 0 and y = -1

Thus,

=> y = ax + b

=> -1 = a•0 + b

=> -1 = 0 + b

=> b = -1

Now,

Putting b = -1 in eq-(1) , we get ;

=> a = b - 3

=> a = -1 - 3

=> a = -4

Thus,

=> f(x) = ax + b

=> f(x) = -4x - 1

Thus,

Required answer is ;

f(x) = - 4x - 1