Let f be a linear function from Z into Z such that (1,1),(2,3),(0,-1) and (-1,-3) `in`f. Find f(x).

Let y=f(x) be a differentiable function such that f(−1)=2,f(2)=−1 and f(5)=3 If the equation f (x)=2f(x) has real root. Then find f(x)

Let f be a linear function with properties f(1)lef(2),f(3)gef(4)and f(5)=5, then which of the following is true

Let f = {(1 ,1), (2, 3), (0, -1), (-1, -3)} be a linear function from Z into Z. Find f (x).

Let f be a one-one function such that f(x).f(y) + 2 = f(x) + f(y) + f(xy), AA x, y in R - {0} and f(0) = 1, f'(1) = 2 . Prove that 3(int f(x) dx) - x(f(x) + 2) is constant.

If f(x) is monotonically increasing function for all x in R, such that f''(x)gt0andf^(-1)(x) exists, then prove that (f^(-1)(x_(1))+f^(-1)(x_(2))+f^(-1)(x_(3)))/(3)lt((f^(-1)(x_(1)+x_(2)+x_3))/(3))

If f'(x)=x^2-1/x^2 and f(1)=1/3 , find f(x).

Let F:RtoR be a thrice differntiable function. Suppose that F(1)=0,F(3)=-4 and F'(x)lt0 for all x epsilon(1,3) . Let f(x)=xF(x) for all x inR . Then the correct statement(s) is (are)

Let f(x) be a real valued periodic function with domain R such that f(x+p)=1+[2-3f(x)+3(f(x))^(2)-(f(x))^(3)]^(1//3) hold good for all x in R and some positive constant p, then the periodic of f(x) is

Let f:[1,oo] be a differentiable function such that f(1)=2. If 6int_1^xf(t)dt=3xf(x)-x^3 for all xgeq1, then the value of f(2) is

if f'(x) = 3x^2-2/x^3 and f(1)=0 , find f(x).