Question

Let $f = \\{ (1,1),(2,4),(0,- 2),(-1,- 5) \\}$ be a linear function from $Z$ into $Z$ . Then, $f (x)$ is

• A. $f(x) = 3x - 2$
• B. $f(x) = 6x - 8$
• C. $f(x) = 5x - 2$
• D. $f(x) = 7x + 2$

Answer 1

Answer: (A)

$f(x) = 3x - 2$

Answer 2

f=\left\\{\left(1, 1\right), \left(2,4\right), \left(0, -2\right), \left(-1,-5\right)\right\\}
Let the linear function is,
$y=mx+c \ldots\left(i\right)$
Then, at $\left(1, 1\right), 1=m+c \ldots\left(ii\right)$
at $\left(0, -2\right), -2=c$,
then $m=3$
Hence, the linear expression becomes
$y=f \left(x\right)=3x-2$