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Question

Let f′′(x)>0xR and g(x)=f(2x)+f(4+x). Then, g(x) is increasing in

A
(,1)
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B
(,0)
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C
(1,)
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D
none of these
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Solution

The correct option is C (1,)
f′′(x)>0xRf(x) is increasing xR
Now g(x)=f(2x)+f(4+x)
If g(x)>0, then f(4+x)>f(2x)
4+x>2x [f(x) is increasing xR]
2x>2 or x>1
g(x) is increasing in (1,).

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