Question

Let f = {(−1, 3),(0,−1),(2,−9)} be a linear function from Z $\to$ Z . Find f (x).

• A. 4x-1
• B. -4x-1
• C. -4x+1
• D. 4x+1

Answer 1

The correct option is B -4x-1

Since f is a linear function
Let f(x)= ax + b
Putting value of x and y in f(x)
Now, for (-1,3)
f(-1) = a(-1) + b
$\Rightarrow$ 3 = -a + b.......(i)
Also for (0,-1)
f(0) = a(0) + b
$\Rightarrow$ -1 = b....(2)
Substituting b = -1 in (i)
we get, a = -4
Substituting the value of a and b in f(x) = ax + b.
Hence the required function is:
f(x)= -4x-1