Square Root Function
A function f from [latex]\mathbb{R}[/latex] to [latex]\mathbb{R}[/latex] in which the variable appears in the radicand of a radical of order 2.
The square root function is sometimes called a radical function of order 2 or a root function of order 2.
The basic form of the rule of a square root function is [latex]f(x) = \sqrt{x} [/latex].
The standard form of the rule of the square root function is [latex]f(x) = a\sqrt{b(x − h)} + k [/latex] where a is not equal to zero and b > 0.
The square root function is a particular case of an nth root function.
Example
Consider the function f(x)=[latex]2\sqrt{0.5\left ( x - 3 \right )} + \left ( -1 \right )[/latex]
Educational notes
- The square root function, also called a radical function of order 2, is derived from the reciprocal relation of the second-degree polynomial function. Although this reciprocal relation is not a function, two square root functions may be derived from it : one positive and one negative.
- For example, if f is a polynomial function defined by the relation y = 0.5x[latex]^{2}[/latex] + 20, then the reciprocal relationship is obtained by interchanging the two variables: x = 0.5y[latex]^{2}[/latex] + 20. By isolating y, we obtain : y = ± [latex] \sqrt{2x - 40} [/latex].