Let `f(x)=x^(2)-x-3=0`.Given `f(a)=0`; then the value of `(a^(3)+1)/(a^(5)-a^(4)-a^(3)+a^(2))` equals

Let f(x)=x^(5)+2x^(3)+3x+4 then the value of 28(d)/(dx)(f^(-1)) at x=-2 is

Let y=f(x)=4x^(3)+2x-6 , then the value of int_(0)^(2)f(x)dx+int_(0)^(30)f^(-1)(y)dy is equal to _________.

If f(x)=int(3x^(2)+1)/((x^(2)-1)^(3))dx and f(0)=0, then the value of (2)/(f(2))| is

For x in R , x ne0, 1, let f_(0)(x)=(1)/(1-x) and f_(n+1)(x)=f_(0)(f_(n)(x)),n=0,1,2….. Then the value of f_(100)(3)+f_(1)((2)/(3))+f_(2)((3)/(2)) is equal to

"If "f(x)=(x-1)^(4)(x-2)^(3)(x-3)^(2)(x-4), then the value of f'''(1)+f''(2)+f'(3)+f'(4) equals

Let f:R rarr R be a continuous function and f(x)=f(2x) is true AA x in R .If f(1)=3 then the value of int_(-1)^(1)f(f(x))dx is equal to (a)6(b) 0 (c) 3f(3)( d) 2f(0)

If the normal to differentiable curve y=f(x) at x=0 be given by the equation 3x-y+3=0, then the value of lim_(x rarr0)(x^(2))/(f(x^(2))-5f(4x^(2))+4f(7x^(2))) is

If the function f(x), defined as f(x)={{:((a(1-xsinx)+b cosx+5)/(x^(2)),":", xne0),(3,":",x=0):} is continuous at x=0 , then the value of (b^(4)+a)/(5+a) is equal to

Given f(x)=Sgn(x^(3)-6x^(2)+12x-14) then the value of f(2)-f(0) is equal to

Let ^(*)f(x)={x^(^^)2;0=3' then