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Question

If f:RR defined by f(x)=x,x<1x2,1x48x,x>4
, then f1(x) is

A
f1(x)=⎪ ⎪ ⎪⎪ ⎪ ⎪x,x<1x,1x16x264,x>16
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B
f1(x)=⎪ ⎪ ⎪⎪ ⎪ ⎪x,x<1x,1x4x24,x>4
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C
f1(x)=⎪ ⎪ ⎪⎪ ⎪ ⎪x,x<1x,1x8x28,x>8
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D
f1(x)=⎪ ⎪ ⎪⎪ ⎪ ⎪x,x<1x,1x4x264,x>4
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Solution

The correct option is A f1(x)=⎪ ⎪ ⎪⎪ ⎪ ⎪x,x<1x,1x16x264,x>16
It can be inferred from the options that f is a bijective function.
Given f(x)=x,x<1x2,1x48x,x>4

Let f(x)=yx=f1(y) (1)
x=⎪ ⎪ ⎪⎪ ⎪ ⎪y,y<1y,1y4y264,y264>4f1(y)=⎪ ⎪ ⎪⎪ ⎪ ⎪y,y<1y,1y16y264,y>16f1(x)=⎪ ⎪ ⎪⎪ ⎪ ⎪x,x<1x,1x16x264,x>16

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