Unlocking The Power Of The Square Root Function: Key Properties And Real-World Applications

Square Root Function

f(x) = √x

The square root function is a mathematical function that represents the square root of a number. It is denoted using the symbol √ followed by the number or variable inside the square root.

For example, the square root of 25 can be written as √25, which gives the answer 5. Similarly, the square root of 9 can be written as √9, which gives the answer 3.

In mathematical terms, the square root function is denoted as follows:

y = √x

Here, x is the number or variable inside the square root and y represents the square root of x.

One important thing to note about the square root function is that it is only defined for non-negative real numbers. This means that the square root of a negative number is undefined in the real number system.

The square root function is a widely used function in mathematics, especially in geometry and trigonometry. It is also used in many real-world applications, such as in finance, statistics, and physics.

Some key properties of the square root function include:

1. The domain of the function is all non-negative real numbers.
2. The range of the function is all non-negative real numbers.
3. The graph of the function is a curve that starts at the origin, continues on the positive x-axis, and increases as x increases.
4. The function is continuous and differentiable for all non-negative real numbers.
5. The inverse function of the square root function is the square function.

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