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Question

If there are exactly two distinct linear functions which map's from [1,1] to [0,2]. Then those functions are

A
x+1
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B
x+1
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C
x1
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D
1x
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Solution

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

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