Understanding the Square Root Function: Properties, Notation, and Examples

Square Root Function

The square root function is a mathematical function that calculates the square root of a given number

The square root function is a mathematical function that calculates the square root of a given number. The symbol used to represent the square root of a number is √.

The square root function can be denoted as follows:

f(x) = √x

Here, f(x) represents the output of the function when the input is x. The square root function takes a positive number as input and returns the positive number whose square equals the given input.

For example:

If we consider the square root of 16, the square root function will output 4, since 4*4 = 16.

If we consider the square root of 9, the square root function will output 3, since 3*3 = 9.

Some key properties of the square root function include:

1. Non-negative output: The square root function always returns a non-negative number, as it is not defined for negative inputs. This means that √x ≥ 0 for all input values of x.

2. Single-valued function: The square root function is a single-valued function, meaning that for each positive input x, there is a unique output value.

3. Domain and range: The domain of the square root function is the set of non-negative real numbers, [0,∞). The range of the function is also the set of non-negative real numbers, [0,∞).

4. Principal square root: The square root function returns the principal square root, which is always the positive square root.

5. Squaring the result: If we square the output of the square root function, we will get x. In other words, (√x)^2 = x for all non-negative input values of x.

It’s important to note that the square root function is different from the absolute value function. While the square root function returns the positive square root, the absolute value function returns the magnitude or distance from zero for any real number input.

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