## Friday, July 13, 2012

A radical function is any function that contains a variable inside a root. This includes square roots, cubed roots, or any nth root , for example f(x) = √(x+5) , g(x) = ∜(x-2) etc.

Here we will discuss about functions involving independent variable inside a square root sign or square root functions. In general the form of a square root function is                 f(x)=a√(x-b)+c , where a , b and c are some real numbers.

Graph of such a function is shown in the applet below.

To find domain of a square root function , the term inside the radical must be equal to or greater than zero, otherwise it is undefined. This means that only the x values that make the term inside the radical positive are defined and in the domain.
For example , f(x) = √(x-4) + 3.

Since (x-4) is inside the radical, the domain lies on all the points where x makes (x-4) greater than or equal to zero.
x-4 ≥ 0
x ≥ 4

So the domain of the function is [4, ∞).

The range of the function is then all the points of the y-axis that we get by putting x values of the domain. Let us start at the point x=4 and put it into the equation. f(x)=√(4-4)+3=3.

Now it can be easily concluded that by putting in any number greater than 4 for x we get f(x) larger than 3, so the smallest number in the range is 3. Thus we see that for any x value above 4 the function is defined. Therefore the range is [3,∞).

This is a Java Applet created using GeoGebra from www.geogebra.org - it looks like you don't have Java installed, please go to www.java.com

#### 1 comment:

1. Functions is a very wide topic with all mathematical quantities described in the form of a functions like the sin,cos,tan,whole number,natural numbers and positive numbers etc.So there is a large number of questions are made from this topic.And that is why its my favorite topic.