Let `g(x)=x^(2)-2x-2` and `f(x)=x^(2)+x+alpha`. If `f(g(x))=0` has no real solution then the set of values of `alpha` is.

If the function f(x) = x^(2) + alpha//x has a local minimum at x=2, then the value of alpha is

Let f(x)=x^(107)+x^(53)+7x+2 . If g(x) is inverse of function f(x) , then the value of f(g'(2)) is

Consider f(x)=|x^(2)-5x+4|, the value of 4 alpha for f(x)=alpha has 3 solutions is

Let f(x) be defined as f(x)={tan^(-1)alpha-5x^(2),0 =1 if f(x) has a maximum at x=1, then find the values of alpha.

Let g(x)=2f((x)/(2))+f(1-x) and f'(x)<0 in 0<=x<=1 then g(x)

Let f(x)=x^(2)+xg'(1)+g''(2) and g(x)=f(1).x^(2)+xf'(x)+f''(x) then

Let f(x)=|x-2| and g(x)=|3-x| and A be the number of real solutions of the equation f(x)=g(x),B be the minimum value of h(x)=f(x)+g(x),C be the area of triangle formed by f(x)=|x-2|,g(x)=|3-x| and x and x- axes and alpha

Let f(x)=|x2| and g(x)=f(f(f(f....(f(x)))..). If the equation g(x)=k,k in(0,2) has 8 distinct solutions then the value n is equal to

Let f(x)=x^(2)+bx+c and g(x)=x^(2)+b_(1)x+c_(1) Let the real roots of f(x)=0 be alpha, beta and real roots of g(x)=0 be alpha +k, beta+k fro same constant k . The least value fo f(x) is -1/4 and least value of g(x) occurs at x=7/2 The roots of g(x)=0 are