Let `f(x)+f(y)=f(xsqrt(1-y^2)+ysqrt(1-x^2))[f(x)` is not identically zero]. Then `f(4x^3-3x)+3f(x)=0` `f(4x^3-3x)=3f(x)` `f(2xsqrt(1-x^2)+2f(x)=0` `f(2xsqrt(1-x^2)=2f(x)`

If f(x)=3x^(2)-2x+4,f(-2)=

If f(x)=1-4x , and f^(-1)(x) is the inverse of f(x), then f(-3)f^(-1)(-3)=

Let y=f (x) and x/y (dy)/(dx) =(3x ^(2)-y)/(2y-x^(2)),f(1)=1 then the possible value of 1/3 f(3) equals :

If 2f(x^2)+3f(1/x^2)=x^2-1 , then f(x^2) is

if f(x)=3e^(x^2) then f'(x)-2xf(x)+1/3f(0)-f'(0)

If f(x)=2xsqrt(1-x^(2)) , then show that f(sin""(x)/(2))=sinx .

Let f(x)=x^(2)-2xandg(x)=f(f(x)-1)+f(5-f(x)), then

If f(x) = (1)/(cos^2xsqrt(1-tan x)) then its anti-derivative F(x) satisfying F(0) = 4 is:

A function f: RvecR satisfies sinxcosy(f(2x+2y)-f(2x-2y)=cosxsiny(f(2x+2y)+f(2x-2y))dot If f^(prime)(0)=1/2,t h e n a)f^('')(x)=f(x)=0 b)4f^('')(x)+f(x)=0 c)f^('')(x)+f(x)=0 d)4f^('')(x)-f(x)=0

f(x)+f(y)=f((x+y)/(1-xy)) ,for all x,yinR . (xy!=1) ,and lim_(x->0) f(x)/x=2 .Find f(1/sqrt3) and f'(1) .