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)`

The interval in which y=x^2""e^(-x) is increasing is (A) (-oo,""""oo) (B) ( 2, 0) (C) (2,""""oo) (D) (0, 2)

Let f(x)=x^2 and g(x) = 2x + 1 be two real functions. find (f +g)(x) , (f-g)(x) , (fg)(x) , (f/g)(x) .

Let f(x) = x^(2) + 2x +5 and g(x) = x^(3) - 1 be two real functions. Find (f+g)(x), (f-g)(x), (fg)(x) and ((f)/(g))(x) .

For the equation cos^(-1)x+cos^(-1)2x+pi=0 , the number of real solution is (A)1 (B) 2 (C) 0 (D) oo

f(x)=(x-2)|x-3| is monotonically increasing in (a) (-oo,5/2)uu(3,oo) (b) (5/2,oo) (c) (2,oo) (d) (-oo,3)

The range of the function f(x)=|x-1| is A. (-oo,0) B. [0,oo) C. (0,oo) D. R

If f : [2,oo) to R be the function defined by f(x)=x^(2)-4x+5, then the range of f is

The domain of the function f(x)=1/(sqrt(|x|-x)) is: (A) (-oo,oo) (B) (0,oo (C) (-oo,""0) (D) (-oo,oo)"-"{0}

If f(x)=int_(0)^(x)log_(0.5)((2t-8)/(t-2))dt , then the interval in which f(x) is increasing is (a) (-oo,2)uu(6,oo) (b) (4,6) (c) (-oo,2)uu(4,oo) (d) (2,6)

Let f(x)= x^2+2ax+b, g(x)=cx^2+2dx+1 be quadratic equation whose graph is shown in figure. It is given that |A.A^'|= |BB^(prime)| and |OA^(prime)|= |OB| If |O A^(prime)|=| AA prime|=1, then the values of ' m ' for which (g(x))^2+mg(x)+4=0 has two real roots which are distinct. (a) (0,4) (b) (4,oo) (c) (4,5) (d) (5,oo)