Question

# If there are exactly two distinct linear functions which map's from [âˆ’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+1Since 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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