A function `g(x)` is defined `g(x)=2f(x^2/2)+f(6-x^2),AA x in R` such `f''(x)> 0, AA x in R`, then m`g(x)` has

Let g'(x)>0 and f'(x)<0AA x in R, then

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

If g(x) =2f(2x^3-3x^2)+f(6x^2-4x^3-3) AA x in R and f''(x) gt 0 AA x in R then g(x) is increasing in the interval

If g(x) =2f(2x^3-3x^2)+f(6x^2-4x^3-3) AA x in R and f''(x) gt 0 AA x in R then g(x) is increasing in the interval

A function f : R -> R^+ satisfies f(x+y)= f(x) f(y) AA x in R If f'(0)=2 then f'(x)=

The function g is defined by g(x)=f(x^(2)-2x+8)+f(14+2x-x^(2)) where f(x) is twice differentiable function, f''(x)>=0 , AA x in R .The function g(x) is increasing in the interval

If g(x)=2f(2x^(3)-3x^(2))+f(6x^(2)-4x^(3)-3)AA x in R and f'(x)>0AA x in R then g(x) is increasing in the interval

Let f(x+y)=f(x)+f(y) and f(x)=x^2g(x)AA x,y in R where g(x) is continuous then f'(x) is

Let f(x+y)=f(x)+f(y) and f(x)=x^(2)g(x)AA x,y in R where g(x) is continuous then f'(x) is