# Explain the meaning of domain and range by finding it in the following function. {(x,y) | y = √x^2 - 1}Show complete solution to explain the answer.

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### 1 Answer

The domain of a function is the set of all x values that make the function to exist.

In this case, the expression of the function is a square root. The square root is defined if and only if it's radicand is positive or, at least, zero.

We'll establish the domain of function:

`x^(2)` - 1`>=` 0

The inequality is positive if the values of x belong to the reunion of intervals (-`oo` ; -1] U [1 ; +`oo` ).

Therefore the domain of the given function is the real set of numbers, except the values within the opened interval (-1 ; 1).

The range of function represents the set that comprises all the values that we get when we plug in x values.

Since the values we can get for y are positive, therefore, the range of function is the interval [0 ; +`oo` ).

**The domain of function is the set of real numbers, except the values within the interval (-1 ; 1) and the range of function is the interval [0 ; +`oo` ).**