What is singleton domain function?

Complete step-by-step answer: Now, a singleton set is defined as a set that contains only one element. Thus the co-domain can contain more than one element. Similarly one-one and bijective function can also contain more than one element. Thus the function is a constant function.

How do you know if a function is left or right?

A function f is said to be continuous from the right at a if lim f (x) = f (a). A function f is said to be continuous from the left at a if lim f (x) = f (a). A function f is said to be continuous on an interval if it is continuous at each and every point in the interval.

What is a singleton set Give an example of a singleton set?

In mathematics, a singleton, also known as a unit set, is a set with exactly one element. For example, the set {null } is a singleton containing the element null. The term is also used for a 1-tuple (a sequence with one member).

What is singleton set example?

A singleton set is a set containing exactly one element. For example, {a}, {∅}, and { {a} } are all singleton sets (the lone member of { {a} } is {a}). The cardinality or size of a set is the number of elements it contains.

What is the domain and range of f(x) = 2x?

The domain and range of this function f (x) = 2x is given as domain D = {x ∈ N } , range R = { (y): y = 2x} A domain refers to “all the values” that go into a function. The domain of a function is the set of all possible inputs for the function.

What is the domain and range of some special functions?

Let’s understand the domain and range of some special functions through examples. The function y = ax,a ≥ 0 y = a x, a ≥ 0 is defined for all real numbers. Hence, the domain of the exponential function is the entire real line. The exponential function alw ays results in a positive value.

How do you find the domain of a constant function?

Let the constant function be f (x) = k f (x) = k. The domain of a constant function is given by R R, that is, the set of real numbers. The range of a constant function is given by the singleton set, k k. 5.

Which function is continuous at all real numbers greater than 1?

Thus, the function f (x) is continuous at all real numbers less than 1. Thus, the function f (x) is continuous at all real numbers greater than 1. Consider c = 1, now we have to find the left-hand and right-hand limits. Here, the left-hand limit is not equal to the right-hand limit.