If f(x) be continuous function for all real values of x and satisfies,
`x^2+{f(x)-2}x+2sqrt3-3-sqrt3.f(x)=0, AA x in R`.Then find the value of `f(sqrt3)`.

x^2+sqrt(3).f(x)+2sqrt(3)-3=0 , then the value of f(sqrt(3))

Let f(x) be a twice differentiable function for all real values of x and satisfies f(1)=1,f(2)=4,f(3)=9. Then which of the following is definitely true? (a). f''(x)=2AAx in (1,3) (b) f''(x)= 5 for some x in (2,3) (c) f''(x)=3AAx in (2,3) (d) f''(x)=2 for some x in (1,3)

If f(x)=sqrt2x-sqrt(2/x)+(4-x)/(4-x) , find the value of f(2)

If 2f(x) + 3f(-x) = 15 - 4x for all real values of x , then show that f(x) = 3 + 4x.

Find the domain and the range of f(x)=sqrt(x^2-3x.)

If f(x) = 2x^(3)-3x^(2)+ 4x - 2 , find the value of f'(-2) .

A continuous real function f satisfies f(2x)=3f(x)AAx in RdotIfint_0^1f(x)dx=1, then find the value of int_1^2f(x)dx

If a continuous function f on [0, a] satisfies f(x)f(a-x)=1, a >0, then find the value of int_0^a(dx)/(1+f(x))

If f(x)=x sqrt(x^(2)+a^(2))+a^(2) log(x+sqrt(x^(2)+a^(2))) , then find the value of f'(0) .

If f(x)=0 and g(x)=f(x)sqrt(1-2(f(x))^2) are strictly increasing AAx in R , then find the values of f(x)dot