How to find the domain and range of a square root function?

The square root of a number is the number that gets multiplied to itself to give the product. 

Answer: Domain: {x : x > or = 0}, Range: {y : y is an element of all real numbers, both positive and negative}.

Explanation:

If you graph the square root function, you are probably doing it in the XY plane, which means there are no i's, which means that for √x to be real, x must be greater than 0. You can conclude using the properties of the square root function.

The domain of the square root function is {x : x > or = 0}

Now we have to think about what the square root function does. Returns the main root as output, that is, the positive number that squared gives the input. So we know that y will be greater than or equal to 0. So, the range of the square root function is y ≥ 0.

Let us understand by taking an example.

y = √ (x + 4) [ random example assumed ]

According to the definition of square root function, x + 4 must be greater than or equal to 0

i.e x + 4 ≥ 0

⇒ x ≥ -4 [ shifting to RHS ]

hence for all the values of x which is greater than or equal to -4, the given square root function is defined.

The range of the square root function is {y: y is an element of all real numbers, both positive and negative}

Thus, The Domain is {x : x > or = 0}, The Range is {y : y is an element of all real numbers, both positive and negative}.