The correct options are
A x+1
B −x+1
Since there are exactly two distinct linear functions which map's from [−1,1] to [0,2].So, Range =[0,2]
Let required linear function be f(x)=ax+b
For a linear function f(x)=ax+b, in the interval [x1,x2],we know that
(i) range is [f(x1),f(x2)], if a>0
(ii) range is [f(x2),f(x1)], if a<0
Case (i):If a>0,
f(−1)=0,f(1)=2
⇒−a+b=0,a+b=2
⇒a=1,b=1
Case (ii):If a<0,
f(−1)=2,f(1)=0
−a+b=2,a+b=0
⇒ a=−1,b=1
∴ Required functions are f(x)=x+1 (or) −x+1