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Question

Consider the functions f(x)={x+1, x12x+1, 1<x2

g(x)={x2, 1x<2x+2, 2x3

Domain of f(g(x)) is

A
[1,2]
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B
[0,2]
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C
[2,2]
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D
[1,2]
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Solution

The correct option is D [1,2]
f(g(x))={g(x)+1g(x)12g(x)+11<g(x)2

Now from graph of g(x),
g(x)1
x[1,1 ]
and g(x)(1,2]x(1,2]

f(g(x))={g(x)+1,x[1,1]2g(x)+1,x(1,2 ]


={x2+1,x[1,1]2x2+1,x(1,2 ]

So, domain of f(g(x))=[1,2]

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