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Question

Let f(x)={1+x,0x23x,2<x3 then f{f(x)}=

A
2+x,0x12x,1<x24x,2<x3
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B
{2+x,0x24x,2<x3
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C
{2+x,0x22x,2<x3
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D
none of these
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Solution

The correct option is A 2+x,0x12x,1<x24x,2<x3
f(x)={1+x,0x23x,2<x3f{f(x)}={1+f(x),0f(x)23f(x),2<f(x)3=⎪ ⎪ ⎪ ⎪⎪ ⎪ ⎪ ⎪1+(1+x),01+x2 & 0x23(1+x),2<1+x3 & 0x21+(3x),03x2 & 2<x33(3x),2<3x3 & 2<x3=2+x,0x12x,1<x24x,2<x3

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