Understanding the Square Root Function: Properties, Graph, Evaluating, and Inverse Function

the square root function

The square root function is a mathematical function that returns the non-negative square root of a given number

The square root function is a mathematical function that returns the non-negative square root of a given number. It is denoted using the symbol √, or as a power of 1/2.

The general form of the square root function is:

f(x) = √x

In this function, x represents the input or the number for which we want to find the square root, and f(x) represents the output or the value of the square root.

The square root function has certain properties that are important to understand:

1. Domain: The square root function is defined for non-negative real numbers. So, the domain of the function is x ≥ 0.

2. Range: Since the square root of any non-negative number is always a non-negative number, the range of the square root function is also x ≥ 0.

3. Graph: The graph of the square root function is a curve that starts at the origin (0, 0) and extends to the right. It approaches the x-axis but never touches it. The graph is symmetric with respect to the y-axis, meaning that if (a, b) is a point on the graph, then (-a, b) is also on the graph.

4. Square root of a negative number: The square root of a negative number is not a real number. In mathematics, the imaginary unit i is used to represent the square root of -1. Therefore, if you are asked to find the square root of a negative number, you may encounter the imaginary unit i in the solution.

To evaluate the square root of a number, simply substitute the number into the function:

– For example, if you want to find the square root of 9, you would substitute 9 into the function:

f(9) = √9 = 3

So, the square root of 9 is 3.

– Similarly, if you want to find the square root of 25, you would substitute 25 into the function:

f(25) = √25 = 5

So, the square root of 25 is 5.

It is important to note that the square root function is the inverse function of the square function (f(x) = x^2).

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