If `f(x)=x^2+2bx=2c^2` and `g(x)=-x^2-2cx+b^2` are such that min `f(x)gtmaxg(x),` then the relation between b and c is

If f(x) = x^2+2bx+2c^2, g(x)=-x^2-2cx+b^2 , such that min f(x)gytmaxg(x) ,then

Let f (x)=x^2+b_1x+c_1 and g(x)=x^2+b_2x+c_2 . When f(x)=0 then the real roots of f(x) are alpha,beta and when g(x)=0 then the real roots of g(x) are alpha+h,beta+h . Minimum value of f(x) is 1/4 and when x= 7/2 then value of g(x) will be minimum. Value of b_2 is-

Let f (x)=x^2+b_1x+c_1 and g(x)=x^2+b_2x+c_2 . When f(x)=0 then the real roots of f(x) are alpha,beta and when g(x)=0 then the real roots of g(x) are alpha+h,beta+h . Minimum value of f(x) is -1/4 and when x= 7/2 then value of g(x) will be minimum. Minimum value of g(x) is-

Let f (x)=x^2+b_1x+c_1 and g(x)=x^2+b_2x+c_2 . When f(x)=0 then the real roots of f(x) are alpha,beta and when g(x)=0 then the real roots of g(x) are alpha+h,beta+h . Minimum value of f(x) is -1/4 and when x= 7/2 then value of g(x) will be minimum. Roots of g(x)=0 are-

If g(x)=x^(2)+x-2 and (g o f)(x)=2(2x^(2)-5x+2) , then f(x)=

If f(x)=e^(x+a) , g(x)=x^(b^2) and h(x)=e^(b^2x) ,show that (g[f(x)])/(h(x))=e^(ab^2)

If f(x)=x^2+x+3/4 and g(x)=x^2+a x+1 be two real functions, then the range of a for which g(f(x))=0 has no real solution is (A) (-oo,-2) (B) (-2,2) (C) (-2,oo) (D) (2,oo)

If f(x)=ax^(2)+bx+c and f(x + 1) = f(x) + x + 1, then determine the values of a and b.

If f(x)=(x^(2)+3x+2)(x^(2)-7x+a) and g(x)=(x^(2)-x-12)(x^(2)+5x+b) , then the value of a and b , if (x+1)(x-4) is H.C.F. of f(x) and g(x) is (a) a=10 : b=6 (b) a=4 : b=12 (c) a=12 : b=4 (d) a=6 : b=10

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