In a function `2f(x)+ xf(1/x)-2f(|sqrt2sin(pi(x+1/4))|)=4cos^2[(pix)/2]+xcos(pi/x)`. Prove that: 1. f(2)+f(1/2)=1 2. f(2)+f(1)=0

In a function 2f(x)+xf((1)/(x))-2f(|sqrt(2)sin(pi(x+(1)/(4)))|)=4cos^(2)[(pi x)/(2)]+x cos((pi)/(x)). Prove that: 1.f(2)+f(1/2)=12*f(2)+f(1)=0=4cos^(2)[(pi x)/(2)]+x cos((pi)/(x))

A function y=f(x) satisfies f(x)=-(1)/(x^(2))-pi^(2)sin(pi x);f'(2)=pi+(1)/(2) and f(1)=0. The value of f((1)/(2))

A function y=f(x) satisfies f''(x)=-(1)/(x^(2))-pi^(2)sin(pi x)f'(2)=pi+(1)/(2) and f(1)=0 then value of f((1)/(2)) is

If x^(4)f(x)-sqrt(1-sin2 pi x)=|f(x)|-2f(x) then f(-2) equals

Let f:R rarr R be a function such that f(x)=x^(3)+x^(2)f'(1)+xf''(2)+f''(3) Consider the following : 1. f(2)=f(1)-f(0) 2. f''(2)-2f'(1)=12 Which of the above is/are correct?

Let f:RtoR be a function such that f(x)=x^(3)+x^(2)f'(1)+xf''(2)+f'''(3) for x in R Consider the following 1. f(2)=f(1)-f(0) 2.f''(2)-2f'(1)=12 Which of the above is/are correct ?

If f(x)=sin(2x^(2)-2[x]) for 0

Let f and g be two differentiable functins such that: f (x)=g '(1) sin x+ (g'' (2) -1) x g (x) = x^(2) -f'((pi)/(2)) x+ f'(-(pi)/(2)) If phi (x) =f ^(-1) (x) then phi'((pi)/(2) +1) equals to :

If f(x) is continuous at x=pi/2 , where f(x)=(sqrt(2)-sqrt(1+sin x))/(cos^(2)x) , for x!= pi/2 , then f(pi/2)=