The Comprehensive Guide to Square Root Function: Properties, Applications, and Graphs

Square Root Function

f(x)=√x

The square root function is a type of mathematical function that uses the square root symbol (√) to indicate the inverse of the square of a number. That is, the square root of a number x is the number that, when multiplied by itself, gives x. The square root function is denoted by the symbol f(x) = √x.

The domain of the square root function is all non-negative real numbers, since the square root of a negative number is not a real number. The range of the function is all non-negative real numbers.

The graph of the square root function is a curve that starts at the origin and continues to rise as x increases. The curve never falls below the x-axis, since the square root of a negative number is not a real number, and approaches infinity as x increases.

Some properties of the square root function include:
– The square root of a positive number is always positive.
– The square root of 0 is 0.
– The square root function is an odd function, which means that f(-x) = -f(x).
– The square root function is a one-to-one function, which means that each input value (x) corresponds to exactly one output value (√x).

Applications of the square root function can be found in various fields such as science, engineering, and finance. For example, in physics, the square root function can be used to calculate the velocity of a moving object based on its kinetic energy. In finance, the square root function can be used to calculate the standard deviation of data sets to determine the risk associated with investments.

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