Square Root Function
A square root function is a mathematical function that takes the square root of a given number
A square root function is a mathematical function that takes the square root of a given number. The square root of a number is the value that, when multiplied by itself, gives back the original number.
The square root function is denoted with the symbol √ and is often written as f(x) = √x or y = √x, where x is the input value and y is the output value. The domain of the square root function is all non-negative real numbers (x ≥ 0) because the square root of a negative number is not a real number.
The graph of a square root function is a curve that starts at the origin (0,0) and increases indefinitely as x increases. It is a half-parabola that opens upward and has a vertical asymptote at x = 0.
Some important properties of the square root function include:
1. Range: The range of the square root function is all non-negative real numbers (y ≥ 0) because the square root of a positive number is always non-negative.
2. Even function: The square root function is an example of an even function, meaning it exhibits symmetry around the y-axis. This is because √x = √(-x) for all x in the domain of the function.
3. Inverse function: The square root function is the inverse of the square function (f(x) = x^2) because applying the square root function to a number and then squaring it will give back the original number.
To evaluate the square root of a number, you can use a calculator or estimation techniques. For example, the square root of 9 is 3 because 3 multiplied by itself equals 9. Similarly, the square root of 25 is 5 because 5 multiplied by itself equals 25.
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