Let `g(x)=f(x)+f(1-x)` and `f^(x)>0AAx in (0,1)dot` Find the intervals of increase and decrease of `g(x)dot`

Let g(x)=f(log x)+f(2-log x) and f'(x)<0AA x in(0,3) Then find the interval in which g(x) increases.

Let g(x)=2f(x/2)+f(2-x) and f''(x)<0 , AA x in (0,2) .Then g(x) increasing in

Let g(x)=2f((x)/(2))+f(1-x) and f'(x)<0 in 0<=x<=1 then g(x)

Let g(x)= f(x) +f'(1-x) and f''(x) lt 0 ,0 le x le 1 Then

Let g(x) = 2 f(x/2)+ f(2-x) and f''(x) lt 0 forall x in (0,2) . Then calculate the interval in which g(x) is increasing.

If (x)=f(x)+f(1-x) and f'(x)<0;0<=x<=1g(x)=f(x)+f(1-x) and f'(x)<0;0<=x<=1 show that g(x) increases in [0,(1)/(2)) and decreases in ((1)/(2),1]

Let f'(sinx)lt0andf''(sinx)gt0,AAx in (0,(pi)/(2)) and g(x)=f(sinx)+f(cosx), then find the interval in which g(x) is increasing and decreasing.

If f(x)+f(1-x)=2 and g(x)=f(x)-1AAx in R , then g(x) is symmetric about

Let f(x)=(sinx)/x and g(x)=|x.f(x)|+||x-2|-1|. Then, in the interval (0,3pi) g(x) is :

Let g(x)=3f((x)/(3))+f(3-x) and f''(x)>0 for all x in(0,3) . If "g" is decreasing in (0,alpha) and increasing in (alpha,3) ,then 8 alpha is :