# List all restricted values sqrt 1 - 3x?

Apr 2, 2017

All values of $x$ so that $x > \frac{1}{3}$

#### Explanation:

We are given $\sqrt{1 - 3 x}$

As we cannot take square root of a negative number,

the restriction on values of $x$ are given by

$1 - 3 x < 0$

or $1 < 3 x$

or $3 x > 1$

or $x > \frac{1}{3}$

Apr 2, 2017

the domain is $\left(- \infty , \frac{1}{3}\right]$
the restricted values are $\left(\frac{1}{3} , \infty\right)$

#### Explanation:

$\sqrt{1 - 3 x}$ => square root can't be negative, it can be zero or greater:
$1 - 3 x \ge 0$ => add $3 x$ to both sides:
$1 \ge 3 x$ => divide both sides by 3:
$\frac{1}{3} \ge x$
Or:
$x \le \frac{1}{3}$ => the domain of the function

to find the restricted values:
$1 - 3 x < 0$
$1 < 3 x$
$x > \frac{1}{3}$