f(x) = (x)^ (1/2)
(i.e. the square root of x)
The only way is to look at the definition of the function. A function is a one-to-one or many-to-one mapping from a set S to a set T, which may be the same as S. These sets need need not be numerical. The domain could be the residents of a town with the range as the first two letters of their first name!Definitional gaps in the domain can always be removed by definition. For example,the function f(x) = 1/x must have a domain that excludes x = 0.However, f(x) = 1/x when x?0, f(0) = 17.3 (for example) does include 0 in its domain.
The domain is whatever you want it to be. In the absence of a domain being defined explicitly, it is taken to be the whole of the real line.
The question cannot be answered for two reasons. The first is that, thanks to the inadequacies of the browser that you are required to use, most mathematical symbols are lost and o we cannot tell what the function is meant to be.Second, the domain and range of any function are interdependent but indeterminate. You can define one of them and the other is determined. For example, whatever the above function, you could choose to have the domain as positive integer values of x. Only. The range would then be determined.
Yes, the domain(input) would be all natural numbers (numbers greater or equal to zero). The range (output) would be all real numbers. -- Not only natural numbers would be considered part of this domain, all negative numbers are also reasonable inputs to this function, as any negative number multiplied by itself would produce a positive number..... The output (range) would therefore be all positive real numbers......
There are infinitely many options. The equation could be a polynomial of degree greater than 1, or it could be a power function, a log function or any combination of these with trig functions. The problem is exacerbated by the fact that there is no clue in the question as to what a stands for.
It could be a subset: for example, for the function y = log(x), the domain is x > 0. There are many functions whose domain is the complex plane.
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.
The only way is to look at the definition of the function. A function is a one-to-one or many-to-one mapping from a set S to a set T, which may be the same as S. These sets need need not be numerical. The domain could be the residents of a town with the range as the first two letters of their first name!Definitional gaps in the domain can always be removed by definition. For example,the function f(x) = 1/x must have a domain that excludes x = 0.However, f(x) = 1/x when x?0, f(0) = 17.3 (for example) does include 0 in its domain.
Find the range of a function by substituting the highest domain possible and the lowest domain possible into the function. There, you will find the highest and lowest range. Then, you should check all the possible cases in the function where a number could be divided by 0 or a negative number could be square rooted. Remove these numbers from the range. A good way to check to see if you have the correct range is to graph the function (within the domain, of course).
The domain is whatever you want it to be. In the absence of a domain being defined explicitly, it is taken to be the whole of the real line.
The question cannot be answered for two reasons. The first is that, thanks to the inadequacies of the browser that you are required to use, most mathematical symbols are lost and o we cannot tell what the function is meant to be.Second, the domain and range of any function are interdependent but indeterminate. You can define one of them and the other is determined. For example, whatever the above function, you could choose to have the domain as positive integer values of x. Only. The range would then be determined.
Any domain that you like. It can be the counting numbers, integers, rationals, reals or complex numbers. Or it can be a subset of any of them. For example, the domain could be {-2, 7, 3.56}.
The domain is what you choose it to be. You could, for example, choose the domain to be [3, 6.5] If the domain is the real numbers, the range is [-12.25, ∞).
It could be either depending on the function that you have.
The domain is the set of values that x may take that gives back an answer that makes sense. The range is the set of values that are possible results of the function. the "log" function does not accept 0 or negative values on its domain and returns negative, zero and positive numbers (ie all real values). The next function does not appear properly but you could figure it out
It most certainly can. In fact it can be quite a useful function. If you want to suppress one function, f(x), over part of its domain you could define another function, g(x) that is equal to zero over that part of the domain and then study the function: h(x) = f(x)*g(x) where both are defined = f(x) otherwise. You may want to do this if f(x) is ill-behaved over a part of its domain.
It could be a function or a linear expression.