domain of f(x)=1/(sqrt(3x+6)) — step-by-step solution

We save the definition:

f (x) = \frac{1}{\sqrt{3 x + 6}}

Let's find the domain of

\frac{1}{\sqrt{3 x + 6}}

For the expression

\frac{1}{\sqrt{3 x + 6}}

to exist, you must check:

3 x + 6 > 0

ⓘ We subtract

6

from both sides

3 x > -6

ⓘ Both sides are divided by

3

x > - \frac{6}{3}

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

3

, their greatest common divisor:

- \frac{6}{3}

-2

▶Domain of definition:

x > -2