Find `/_\^3f(2)` from the following values of `f(x) : f(2) = 9, f(4)=63, f(6)=211, f(8)=506`.

if f(x)=x^2-6 then value of f'(6) is

The graph of y = f(x) is as shown in the following figure. Find the following values (i) f(-3)" "(ii) f(-2)" "(iii) f(0) (iv) f(2)" "(v) f(3)" "(vi) lim_(x to -3) f(x) (vii) lim_(x to 0) f(x)" "(viii)lim_(x to 2) f(x)" "(ix) lim_(x to 3) f(x) (x) lim_(x to 2^(-)) f(x)" "(x i)lim_(x to -2^(+)) f (x)" "(x ii)lim_(x to 0^(-)) f(x) (x iii) lim_(x to 0^(+)) f(x)

For all real values of x and y, if f(x+y)=f(x)f(y), f(5)=4, f'(0)=2, find f'(5).

if 2f(x)+3f(-x)=x^2+x+1 find the value of f'(1)

If f(x) = cos(log_e x) , then find the value of f(x) cdot f(y) - 1/2[f(x/y) + f(xy)]

If f(x)f(y) = f(x) + f(y) + f(xy) -2 for all real values of x and y and f(2) = 5, find f(4) and f(1/4) .

Find the period of the real valued function satisfying f(x)+f(x+4)=f(x+2)+f(x+6)

If f(x)= 4^x/(4^x-2) then find the value f(x)+f(1-x).

If 2f(x) - 3f(1/x) = x^2 (x ne 0) , then find f(2).

Let X = {1, 3, 5, 7} and Y={2, 4, 6, 8}. If f be the rule associating elements of X to elements of Y, such that f(1) = 4, f(3) = 2, f(5) = 8, f(3) = 6, f(7) = 4. State whether f defines a function of X into Y or not.