Question:
The distinct linear functions that map [−1, 1] onto [0, 2] are
(a) $f(x)=x+1, g(x)=-x+1$
(b) $f(x)=x-1, g(x)=x+1$
(c) $f(x)=-x-1, g(x)=x-1$
(d) None of these
Solution:
Let us substitute the end-points of the intervals in the given functions. Here, domain = [-1, 1] and range =[0, 2]
By substituting -1 or 1 in each option, we get:
Option (a):
$f(-1)=-1+1=0$ and $f(1)=1+1=2$
$g(-1)=1+1=2$ and $g(1)=-1+1=0$
So, option (a) is correct.
Option (b):
$f(-1)=-1-1=-2$ and $f(1)=1-1=0$
$g(-1)=-1+1=0$ and $g(1)=1+1=2$
Here, $f(-1)$ gives $-2 \notin[0,2]$
So, (b) is not correct.
Similarly, we can see that (c) is also not correct.