Question

How do you find the domain and range of \[y = \dfrac{1}{{\sqrt x }}\] ?

Answer 1

Hint: According to the question, we have to know the terms like function, domain, range, etc,.A function in Mathematics is relation. This relation is between two sets which associate every element from the first set to exactly one element of the second set.

Complete step-by-step answer:
First, we will try to know about the terms used in the question.
Domain of any function in Mathematics is known to be the set of the possible inputs of the function. This means that the inputs are the values for which the functions are defined.
In this question, the domain is the possible value for \[x\] . Hence, the domain is any real number that is positive where \[x > 0\] . This is because the square root of any number that is negative is imaginary.
Now, we will talk about range. Range of a function in Mathematics, is known to be the set of possible outputs of the function which the function is receiving when it is getting applied to its total set of functions.
In this question, the range is the possible value of \[y\] . Hence, the range is the real number that is positive. But we have an exception here, for \[x = 0\] . This has no meaning when \[x = 0\] .

Note: When we simply define a function and we do not state the domain of that function, then we say that the domain of that function is the largest or biggest subset of the real numbers where the function is defined.