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

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?

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

Let L denotes the number of subjective functions f : A -> B, where set A contains 4 elementset B contains 3 elements. M denotes number of elements in the range of the function f(x) = sec^-1(sgmx) + cosec^-1(sgn x) where sg n x denotes signum function of x. And N denotes coefficient of t^5 in (1+t^2)^5(1+t^3)^8. The value of (LM+N) is lambda, then the value of lambda/19 is

Let f:R^(+)rarr{-1,0,1} defined by f(x)=sgn(x-x^(4)+x^(7)-x^(8)-1) where sgn denotes signum function then f(x) is (1) many- one and onto (2) many-one and into one-one and onto (4) one- one and into

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-

Find the range of f(x)=sgn(x^(2)-2x+3)

Number of points where f(x)=|x-sgn(x)| is non differentiable is (sgn( ) denotes signum function )