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