If `f(x)=max| 2 siny-x`|, (where `y in R`), then find the minimum value of f(x).

Find the minimum value of f(x)=|x+2|+|x-2|+|x|.

Let y=f(x) be the solution of the differential equation (dy)/(dx)+k/7 x tan x=1+xtanx-sinx, where f(0)=1 and let k be the minimum value of g(x) where g(x)="max"|(sqrt(193)-1)/2cosy+cos(y+(pi)/3)-x| where yepsilonR then Area bounded by y=f(x) and its inverse between x=(pi)/2 and x=(7pi)/2 is

If f(x+ y) = f(x) + f(y) for x, y in R and f(1) = 1 , then find the value of lim_(x->0)(2^(f(tan x)-2^f(sin x)))/(x^2*f(sin x))

If the integral int(x^(4)+x^(2)+1)/(x^(2)-x+1)dx=f(x)+C, (where C is the constant of integration and x in R ), then the minimum value of f'(x) is

If f is polynomial function satisfying 2+f(x)f(y)=f(x)+f(y)+f(x y)AAx , y in R and if f(2)=5, then find the value of f(f(2))dot

If f is polynomial function satisfying 2+f(x)f(y)=f(x)+f(y)+f(x y)AAx , y in R and if f(2)=5, then find the value of f(f(2))dot

Let F:R to R be such that F for all x in R (2^(1+x)+2^(1-x)), F(x) and (3^(x)+3^(-x)) are in A.P., then the minimum value of F(x) is:

If f(x+f(y))=f(x)+yAAx ,y in R a n df(0)=1, then find the value of f(7)dot

Consider a differentiable f:R to R for which f(1)=2 and f(x+y)=2^(x)f(y)+4^(y)f(x) AA x , y in R. The minimum value of f(x) is

Let f(x) = Maximum {sin x, cos x} AA x in R . minimum value of f (x) is