# Domain and Range

• Mar 5th 2006, 06:56 AM
batman123
Domain and Range
Please explain the domain and range of a function:

f(x)= square root 6-2x
What is the domain and what is the range :confused:
• Mar 5th 2006, 09:37 AM
CaptainBlack
Quote:

Originally Posted by batman123
Please explain the domain and range of a function:

f(x)= square root 6-2x
What is the domain and what is the range :confused:

The domain of a function is the set (in this case of real number) on which the
function is defined.

The function:

$\displaystyle f(x)=\sqrt{6-2x}$

is defined whenever $\displaystyle 6-2x \ge 0$, which is equivalent to $\displaystyle x \le 3$. Thus the
domain of $\displaystyle f$ is the set of all real numbers $\displaystyle x \le 3$.

The range of a function is the set (in this case of real numbers)of values
which can be a value taken by the function for sone $\displaystyle x$ in its domain.

In this case any $\displaystyle y \ge 0$ can be written as $\displaystyle y=f(x)$ for
some $\displaystyle x \le 3$, so the range of $\displaystyle f$ is the set of all $\displaystyle y \ge 0$.

RonL
• Mar 5th 2006, 09:44 AM
ThePerfectHacker
Quote:

Originally Posted by batman123
Please explain the domain and range of a function:

f(x)= square root 6-2x
What is the domain and what is the range :confused:

Here I graphed it thus you can see which value's x and y can take: