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If f(x)= a^({a^(|x|)sgn x }),g(x)=a^([a^...

If `f(x)= a^({a^(|x|)sgn x }),g(x)=a^([a^(|x|)sgn x]` for ` a gt 1, a!=1` and ` x in R`, where `{**}` & `[**]` denote the fractional part and integral part functions respectively, then which of the following statements holds good for the function `h(x)`, where `(ln a) h(x) = (ln f(x) + ln g(x))`.

A

h' is even and increasing

B

h' is odd and decreasing

C

h' is even and decreasing

D

h' is odd and increasing

Text Solution

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The correct Answer is:
D
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