If `f(x)=a x^2+b x+c` is a quadratic function such that `f(1)=8,f(2)=11` and `f(-3)=6` find `f(x)` by using determinants. Also, find `f(0)dot`

If f(x)=(a x^2+b)^3, then find the function g such that f(g(x))=g(f(x))dot

If f: R->R is an odd function such that f(1+x)=1+f(x) and x^2f(1/x)=f(x),x!=0 then find f(x)dot

Let f (x) be a quadratic function such that f (0) =1 and f(-1)=4, ifint(f(x))/(x^(2)(1+x)^(2))dx is a rational function then the value of f(10)

Let f be a real-valued function such that f(x)+2f((2002)/x)=3xdot Then find f(x)dot

Let f be a real-valued function such that f(x)+2f((2002)/x)=3xdot Then find f(x)dot

If f(x) is a continous function such that f(x)|0,AA x in[2,10] and int_(4)^(8)f(x) dx=0 , then find f (6)

If f(x) is a twice differentiable function such that f(a)=0, f(b)=2, f(c)=-1,f(d)=2, f(e)=0 where a < b < c < d e, then the minimum number of zeroes of g(x) = f'(x)^2+f''(x)f(x) in the interval [a, e] is

If f(x)=A x^2+B x+C then find f '(x)

If f(x) is a polynomial function of the second degree such that, f(-3)=6,f(0)=6" and "f(2)=11 , then the graph of the function, f(x) cuts the ordinate x = 1 at the point

Show that the function f: Q->Q defined by f(x)=3x+5 is invertible. Also, find f^(-1) .