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Question

Which of the following are two distinct linear functions which map the interval [−1,1] onto [0,2]

A
f(x)=1+x or 1x
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B
f(x)=1+2x or 1x
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C
f(x)=1+x or 12x
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D
f(x)=1+x or 2x
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Solution

The correct option is A f(x)=1+x or 1x
Out of two linear functions one will be increasing and other will be decreasing.
Let f(x)=ax+b
For increasing: f(1)=0=>ba=0b=a and f(1)=2a+b=2a=b=1f(x)=1+x
For decreasing: f(1)=2=>ba=2 and f(1)=0a+b=2b=1,a=1f(x)=1x

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