domain of f(x)=sqrt(3-6x) — step-by-step solution

We save the definition:

f (x) = \sqrt{3 - 6 x}

Let's evaluate the domain of

\sqrt{3 - 6 x}

For the expression

\sqrt{3 - 6 x}

to be defined, we must have:

3 - 6 x \geq 0

ⓘ We add

6 x

to both sides

3 \geq 6 x

ⓘ Both sides are divided by

6

x \leq \frac{3}{6}

ⓘ We simplify the fraction by dividing the numerator and the denominator by

3

, their greatest common divisor:

\frac{3}{6}

\frac{1 \cdot 3}{2 \cdot 3}

\frac{1}{2}

▶Domain of definition:

x \leq \frac{1}{2}

The numeric value of:

x \leq \frac{1}{2}

is:

▷

x \leq 0.5