The distinct linear functions that map [−1, 1] onto [0, 2] are

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.

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