Find Domain And Range Of Function

How do I find domain and range of function? Can we find domain from range and range from domain, without graph? Clear my concept I'm confused.

You can find the domain and range of a function quite easily, actually.Basically, the domain of a function is the set of all numbers that you can put into the function (the x-values or input values for the function) and still get a real (as in, not imaginary) solution. And the range is the set of all numbers that could possibly come out from the function by inputting domain values. Simply put, the range is the scope of y-values of the function. So, to answer your question, you can find the range from the domain, providing that you have the function equation.For example, if someone asked you the domain and range of a simple line, say y = x + 4, the domain would equal (negative infinity, positive infinity), since you can substitute in any number for x. Knowing that, we technically substitute negative infinity and positive infinity in for x to find the highest and lowest values for the range. This is also (negative infinity, positive infinity). But the domain and range is not “all real numbers” for all functions- for example, y = sqrt (x - 1). For this function the domain would be [1, positive infinity) and the range would be [0, positive infinity). This is because if we plug in any smaller x-value than 1, we will get a negative square root, which is imaginary. However, we can plug in any value greater than one and still get a real answer. The range is what we get when we plug in the smallest and largest domain values- when we plug in 1, we get zero, and for infinity, we get infinity.EXTRA: Domain and range are uaually denoted using interval notation, which could look like any of these for both the domain and range, but for this example I will just show domain: (smallest value in domain, largest value in domain) OR [smallest value in domain, largest value in domain] OR (smallest value in domain, largest value in domain] OR [smallest number in domain, largest number in domain]. Whether you use a bracket or parenthesis depends on whether the value it is next to is inclusive in the range or not. For example, a range of (2, infinity) would mean that the smallest y-value approaches, but never actually reaches 2 (since there is a parenthesis) and that the function’s output will continue to increase to infinity. Since infinity is not an actual number, we always use the parenthesis next to infinity (and also, you would put the symbol for infinity, not write it out).Hope this helped.

How do you find the domain and range of functions?

Think of a function as a machine. You put a number in, and you get a different number out. Some machines will take any number you give them; others don’t work on some numbers. Some machines will (eventually) spit out just about any number you can imagine; other machines are known to only produce some numbers but not others.“Domain” means the numbers you feed to the function. “Range” means the numbers it gives back to you.For example, think of y=3x. You can plug any number you want in for x, so the domain of this function is “all real numbers” (or everything from negative infinity to positive infinity, if you like). And you can probably figure out that any real number could come out of it too. (You want a certain real number to come out? Plug in one-third of that number for x, and there you go!) So the range of this function is also “all real numbers”.But suppose your function is y=x^2 (the simplest possible quadratic). Your domain is still all real numbers. But any real number, squared, will result in a positive number… so the range would be “all non-negative real numbers” (or, if you prefer, “all positive real numbers and also zero”).In short, if you think of domain as “all possible inputs” and range as “all possible outputs”, you’ll have the right idea.

How can I find the domain and range of a secant function?

Since the secant is the reciprocal of the cosine, it will not exist when the cosine x = 0. Thus, the domain is all x, except …-3π/2, -π/2, π/2, 3π/2, ……. The range will be the reciprocal of the range of the cosine function. Since the cosine has range [-1.1], the range of the secant is (-∞,-1] U [1,∞). If the range doesn’t make sense to you, take some values between -1 and 1 and flip them. You’ll see that the closer you get to zero for the cosine, the secant will get large without bound. For example, cos x could = 1/10000, so the corresponding secant would be 10000/1 or 10,000.

How do I find the domain and range of a function and its inverse?

f(x) = (3x - 7)/5 f^-1(x) = (5y + 7)/3  The DOMAIN is the set of all possible numbers that you can put in for the independent variable and get an answer. If you had g(x) = 1/x,  you could NOT put in 0 for x and get an answer because 1/0 is undefined. So the domain is all numbers but 0. The RANGE is the set of numbers you will get for the dependent variable. If you had g(x) = 1/x,  you could NOT get 0 for g(x), no matter what you put in for x. So the range is all numbers but 0. In both your functions the domain and the range equal all possible numbers. Or all real numbers.  ANSWER Another way to write the answers is: D = {x | x = R}  and  R = {f(x) |  f(x) = R} where D = domain, R = range, { } means set, | is such that ////////////////////////////////////////////////

How do you find the domain and range of composite functions?

The parameter methodIf you have each function given explicitly, say f(x) = x+3 and g(x)=x^2 and you want to find the domain and range of g(f(x)) then the easiest thing to do is form a function in one variable by passing the parameter through. So g(f(x))=g(x+3)=(x+3)^2. Finding the domain and range of this is simple, it's just a normal function. This method applies for higher orders of composition too. However, if you don't have the functions explicitly (we’re not always that lucky) or want to think about it in terms of sets read below.The set methodLet's say our composite function is g(f(x)). The easiest way to determine domain and range is to split the functions up.Start by taking f(x). Determine the range of that function. Take g(x) and determine it's domain. Do this as if they were individual functions - this should be fairly easy.Now take the intersection of those two sets, call it X. This is the set that links the two functions, it is mapable from the domain of g(f(x)) by carrying out f, and its mapable to the range of g(f(x)) by carrying out g.The domain of g(f(x)) is the preimage of X in f, or if you prefer f^-1(X)=Y. The range of g(f(x)) is g(X)=Z.This forms the sequence of equivalences g(f(Y))=g(X)=Z. So Y is the domain and Z is the range. This should be clear by f: Y → X and g: X → Z.This process can be extended to more highly composite functions such as f(g(h(x))) but requires a bit more moving backwards and forwards. I would start by determining the domain and range of g(h(x)) as above. Then carry out the process of intersecting the domain of f with the range of g(h(x)), call it X. You should then be fairly easily be able to get the total range by calculating f(X)=W. You'll then need to work back to determine the final domain of g(h(x)) that is allowable. To do this you carry out the preimage of g on X, I.e. g^-1(X) = Y. Then carry out the preimage of h on Y, I.e h^-1(Y) = Z. This gives the final domain.Written more nicely we will have found h: Z → Y, g: Y → X and f: X → W where Z is the domain and W is the range of f(g(h(x))).I hope this explanation helps. The set methodology requires a bit of thought but after some examples it becomes easier. If anyone has any examples they need help with feel free to comment or request me to answer another question and I'll get round to it.