The function `f(x)=x(x+4)e^(-x//2)` has its local maxima at `x=adot` Then (a)`a=2sqrt(2)` (b) `a=1-sqrt(3)` (c)`a=-1+sqrt(3)` (d) `a=-4`

The range of function f(x) = sqrt(.^(x^2+4x)C_(2x^2+3)) is

If f(x)=sin^2x and the composite function g(f(x))=|sinx| , then g(x) is equal to (a) sqrt(x-1) (b) sqrt(x) (c) sqrt(x+1) (d) -sqrt(x)

The values of parameter a for which the point of minimum of the function f(x)=1+a^2x-x^3 satisfies the inequality (x^2+x+2)/(x^2+5x+6)<0a r e (a) (2sqrt(3),3sqrt(3)) (b) -3sqrt(3),-2sqrt(3)) (c) (-2sqrt(3),3sqrt(3)) (d) (-2sqrt(2),2sqrt(3))

The function f (x) =1+ x ln (x+ sqrt(1+ x ^(2)))-sqrt(1- x^(2)) is:

f(x)=(x-1)|(x-2)(x-3)|dot Then f decreases in (a) (2-1/(sqrt(3)),2) (b) (2,2+1/(sqrt(3))) (c) (2+1/(sqrt(3)),4) (d) (3,oo)

If x^4+1/(x^4)=623 , then x+1/x=? (a)27 (b) 25 (c) 3sqrt(3) (d) -3sqrt(3)

The range of the function f(x) = sqrt(4 - x^2) + sqrt(x^2 - 1) is

A solution of sin^-1 (1) -sin^-1 (sqrt(3)/x^2)- pi/6 =0 is (A) x=-sqrt(2) (B) x=sqrt(2) (C) x=2 (D) x= 1/sqrt(2)

If x=sqrt(5)+\ 2, then x-1/x equals (a) 2sqrt(5) (b) 4 (c) 2 (d) sqrt(5)

If cos^-1 ((x^2-1)/(x^2+1))+ tan^-1 ((2x)/(x^2-1)) = (2pi)/3 , then x equal to (A) sqrt(3) (B) 2+sqrt(3) (C) 2-sqrt(3) (D) -sqrt(3)