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Let g(x)=f(logx)+f(2-logx)a n df^(prime ...

Let `g(x)=f(logx)+f(2-logx)a n df^(prime prime)(x)<0AAx in (0,3)dot` Then find the interval in which `g(x)` increases.

Text Solution

Verified by Experts

The correct Answer is:
(0,e)
`g(x) =f(logx)+f(2-logx)`
`therefore g'(x) =[f(logx)-f'(2-logx)//x]`
g(x) increases if `g(x)gt0` Now `x gt0`
or `f(logx)-f(2-logx)gt0`
or `f(log x) gt f'(2-logx)`
or `log xlt2-logx[f''(x)lt0f,(x)]` is decreasing ]
or `log xlt 1`
or `0ltxlte`
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