If `f''(x)>0` and `Q(x)=2f((x^2)/2)+f(6-x^2),AAx in R ,` then function `Q(x)` is

Discuss the monotonocity of Q(x), where Q(x)=2f((x^(2))/(2))+f(6-x^(2))AA x in R It is given that f'(x)>0AA x in R. Find also the point of maxima and minima of Q(x)

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 mg(x) has

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

Let f_(1) (x) and f_(2) (x) be twice differentiable functions where F(x)= f_(1) (x) + f_(2) (x) and G(x) = f_(1)(x) - f_(2)(x), AA x in R, f_(1) (0) = 2 and f_(2) (0) = 1. "If" f'_(1)(x) = f_(2) (x) and f'_(2) (x) = f_(1) (x) , AA x in R . then the number of solutions of the equation (F(x))^(2) =(9x^(4))/(G(x)) is...... .

If the function / satisfies the relation f(x+y)+f(x-y)=2f(x),f(y)AA x,y in R and f(0)!=0 ,then f(x) is an even function f(x) is an odd function If f(2)=a, then f(-2)=a If f(4)=b, then f(-4)=-b

let f(x)={2,x in Q),(-2,x!in Q), then

Let a function f(x) satisfies f(x)+f(2x)+f(2-x)+f(1+x)=x,AA x in R Then find the value of f(0)

Let f:R to R be a function satisfying f(2-x)=f(2+x) and f(20-x)=f(x) AA x in R. For this function f , answer the following. If f(2) ne f(6), then the

If f:R rarr R is continous function satisying f(0) =1 and f(2x) -f(x) =x, AAx in R , then lim_(nrarroo) (f(x)-f((x)/(2^(n)))) is equal to