Show that range of the function `(1)/(2cosx-1)" is "(-oo,-(1)/(3)]cup[1,oo)`

Find the range of the function (1)/(2cosx-1) .

Find the range of f(x)=1/(2cosx-1)

Find the integrals of the functions (1-cosx)/(1+cosx)

Prove that the solution of (x+1)/(x+3)lt3 " is "(-oo,-4)cup(-3,oo)l.

The domain of the function f(x)=1/(sqrt(|x|-x)) is: (1) (-oo,oo) (2) (0,oo (3) (-oo,""0) (4) (-oo,oo)"-"{0}

Show that the function {{:((x^(3)-1)/(x-1)", ""if "xne1),(3", ""if "x=1):} is continuous on (-oo,oo)

The range of the function f(x)=(x^2+x+2)/(x^2+x+1),x in R , is (1,oo) (b) (1,(11)/7) (c) (1,7/3) (d) (1,7/5)

Consider the equation x^4 + 2ax^3 + x^2 + 2ax + 1 = 0 where a in R . Also range of function f(x)= x+1/x is (-oo,-2]uu[2,oo) If equation has at least two distinct positive real roots then all possible values of a are