The domain is the possible values that can be input into the function and produce a real number output.
In algebra, the domain consists of all possible values for the x variable that could make the function work. The range is all of the possible values of the function, using each number in the domain.
An irrational number.
Yes, every irrational number is also a real number. Real numbers include all the numbers on the number line, which consists of both rational and irrational numbers. Rational numbers can be expressed as fractions, whereas irrational numbers cannot be expressed as simple fractions. So, while all irrational numbers are real numbers, not all real numbers are irrational—some are rational.
Yes, for some functions A, and not for others.
It depends on its domain.
A number does not have a range and domain, a function does.
f(x) = 1 if x is rational f(x) = 0 if x is irrational But there is no specific question about this function. It is a well defined function whose domain is the real numbers and whose codomain consists of the two values, 0 and 1. It is a function with infinitely many discontinuities, and an integral which is 0.
The domain is the possible values that can be input into the function and produce a real number output.
f(x)=5x Domain is any number for x that will provide a real number for f(x). In this function, x can be any real number, and f(x) will be a real number. Thus domain is all real numbers.
Yes. A function is a rule to assign a value based on some other value; you can make the function equal to a constant for all values of a variable "x", or you can make it equal to a few values. Commonly used functions of this type include the integer function (take the integer part of a number), which, if you consider a finite domain (for example, all numbers from 0 to 10), has an infinite number of values in the domain, but only a few specific values in its range; and the sign function.
no
true
Actually the product of a nonzero rational number and another rational number will always be rational.The product of a nonzero rational number and an IRrational number will always be irrational. (You have to include the "nonzero" caveat because zero times an irrational number is zero, which is rational)
yes it is a function because sequence defined as "a function whose domain is set of natural number"
Real numbers which cannot be written in (a/b) form are called as irrational numbers like √3, √5,√2 etc. Now, we discuss applications of irrational numbers:1. Use of pi(π) : pi is an irrational number which is use in many purpose in math like:Area of circle = π * r2 where pi (π) = 3.14 and r is a radius.Circumference of circle = π * d where d is a diameter of circle,2. Use of exponential (e): e is an irrational number which is used in many parts of math-.3. Use of cube root: cube root is basically used to find out area and perimeter of cube and cuboids because both have three dimension structures.4. Use of irrational number to find out domain: irrational numbers are use to find out domain of particular function. For instance, domain of a function lies between 2 and 3 then we can represent them as √5. Similarly when domain lie between 1 and 2 then we represent them as √2 and between 3 and 4, we can represent them as √11 etc.So, irrational numbers are used in finding approx value of any real measurement because it is difficult to find out exact value of real measurement. Irrational numbers are calculating non terminating point of function.For more information visit related links.
Any real number is either rational or irrational. The rational ones are the ones that can be written in the form a/b where and b are integers and b does not equal 0. The irrational ones are all the other ones. If you expand your domain to include numbers other than the real numbers, like the imaginary numbers for example, there is no definition of "rational" or "irrational" for the non-real numbers. Zero is a rational number since it can be written as 0/1 and both 0 and 1 are integers.