`f(x)=3^(-|x|)-3^x+sgn(e^-x)+2` (where sgn x denotes signum function of x). Then which one of the following is correct?

The range of f(x)= 3^(-|x|)-3^(x)+sgn(e^(-x))+2 (where sgn x denotes signum function of x )

Let f:R to R be defined by f(x) = 5^(-|x|) - 5^(x) + sgn (e^(-x)) + 4 where sgn (x) denotes the signum function of x. Then

If f(x)=(x-2)|x-4| sgn(x)AA x in R (Where sgn( x ) denotes signum function) On the basis of above information answer the following questions: f(x) is monotonically increasing in interval-

If f(x)=(x-2)|x-4| sgn(x)AA x in R (Where sgn( x ) denotes signum function) On the basis of above information answer the following questions: f(x) is monotonically increasing in interval-

If f(x)=sgn(cos 2x - 2 sin x + 3) , where sgn () is the signum function, then f(x)

If f(x)=sgn(cos 2x - 2 sin x + 3) , where sgn () is the signum function, then f(x)

If f(x)=sgn(cos 2x - 2 sin x + 3) , where sgn () is the signum function, then f(x)

If f(x)=cos^(-1)(sgn((2[x])/(3x-[x]))) , where sgn ( ) denotes the signum function and [.] dentoes the greatest integer functions, then which of the following is/are correct?

Let f(x)={{:(-3+|x|",",-ooltxlt1),(a+|2-x|",",1lexltoo):} and g(x)={{:(2-|-x|",",-ooltxlt2),(-b+"sgn(x),",2lexltoo):} where sgn(x) denotes signum function of x. If h(x)=f(x)+g(x) is discontinuous at exactly one point, then which of the following is not possible?