`f(x)=sqrt(x)-1/3int_0^xsqrt(x y)f(y)\ dy , AAx in R , xgeq0` then `f(1)=`

If f(x+y+1)={sqrt(f(x))+sqrt(f(y))}^2 and f(0)=1AAx ,y in R ,d e t e r m in ef(n),n in Ndot

If f(x+y+1)={sqrt(f(x))+sqrt(f(y))}^2 and f(0)=1AAx ,y in R ,determine f(n),n in Ndot

y=f(x), where f satisfies the relation f(x+y)=2f(x)+xf(y)+ysqrt(f(x)) , AAx,y epsilon R and f'(0)=0.Then f(6)is equal ______

If f(x)=x+int_0^1(xy^2+x^2y) dy find f(x)

If f(x)=f(x)={(sin(a+1)x+sinx)/(x), ,x<0,c \ at x=0, (sqrt(x+b x^2)-sqrt(x))/(b xsqrt(x)),xgeq0,f(x) is continuous at x=0,t h e n (a). a=-3/2,b=0,c=1/2 (b) a=-3/2,b=1,c=-1/2 (c) a=-3/2,b in R-[0],c=1/2 (d) none of these

A function f: I to I, f(x + y) = f(x) + f(y) - 1/2 AAx, y in I , where f(1) > 0, then f(x) is

A function f: RrarrR satisfies the equation f(x) f(y) - f(xy) = x+ y, AAx,y in R and f(1) gt 0 , then

If f(x)=f(x)={(sin(a+1)x+sinx)/(x^x c),x<0(sqrt(x+b x^2)-sqrt(x))/(b xsqrt(x)),xgeq0,x-0 is continuous at x=0,t h e n a=-3/2,b=0,c=1/2 (b) a=-3/2,b=1,c=-1/2 a=-3/2,b in R-[0],c=1/2 (d) none of these

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)

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)