Let `f(x)` be a function satisfying the condition `f(-x) = f(x)` for all real x. If `f'(0)` exists, then its value is equal to

Let f(x) be a function satisfying f(x) + f(x+2) = 10 AA x in R , then

The curvey y=f(x) which satisfies the condition f'(x)gt0andf''(x)lt0 for all real x, is

A function f(x) satisfies the functional equation x^2f(x)+f(1-x)=2x-x^4 for all real x. f(x) must be

Let f(x) be a function such that f'(a) ne 0 . Then , at x=a, f(x)

Let f be a one-one function satisfying f'(x)=f(x) then (f^-1)''(x) is equal to

Let f be a function satisfying of xdot Then f(x y)=(f(x))/y for all positive real numbers x and ydot If f(30)=20 , then find the value of f(40)dot

Let f be a function satisfying f(x+y)=f(x) + f(y) for all x,y in R . If f (1)= k then f(n), n in N is equal to

Let f(x) be a real valued function satisfying the relation f(x/y) = f(x) - f(y) and lim_(x rarr 0) f(1+x)/x = 3. The area bounded by the curve y = f(x), y-axis and the line y = 3 is equal to

A quadratic function f(x) satisfies f(x)ge0 for all real x. If f(2)=0 and f(4)=12, then the value of f(6) is :

Let f be a differential function satisfying the condition. f((x)/(y))=(f(x))/(f(y))"for all "x,y ( ne 0) in R"and f(y) ne 0 If f'(1)=2 , then f'(x) is equal to