Please explain the domain and range of a function:
f(x)= square root 6-2x
What is the domain and what is the range
The domain of a function is the set (in this case of real number) on which theOriginally Posted by batman123
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