Question

Let $f:[-1,1]\to [0,2]$ be a function such that the range of $f=$ co-domain of $f$, then the number of distinct linear function(s) $f$ is

• A. $3$
• B. $2$
• C. $4$
• D. $0$

Answer 1

The correct option is B $2$

Linear functions are of form
$f\left(x\right)=ax+b$
$\therefore$ linear function is either increasing or decreasing in nature
Now
Case $1:$
$f(-1)=0,f\left(1\right)=2$
$-a+b=0\text{and}a+b=2$
$\therefore a=1,b=1$
$f\left(x\right)=x+1$

Case $2:$
$f(-1)=2,f\left(1\right)=0$
$-a+b=2\text{and}a+b=0$
$\therefore a=-1,b=1$
$f\left(x\right)=-x+1$

Hence, there are $2$ linear functions possible.