Question

If the square root of 1 over 2 x - 10 added by 3, which inequality can be used to find the domain of f(x)?

Answer 1

From the description, we have the function $f(x)= \sqrt{ \frac{1}{2x-10}+3 }$
Since the square root cannot be a negative number, the only thing need to do to find the domain of the function $f(x)$ is take the expression inside the square rot and set it greater or equal than zero:
$\frac{1}{2x-10}+3 \geq 0$
$\frac{6x-29}{2x-10} \geq 0$
$\frac{6x-29}{2(x-5)} \geq 0$
$x \leq \frac{29}{6}$ or $x\ \textgreater \ 5$

We can conclude that we can use the inequality $\frac{1}{2x-10}+3 \geq 0$ to find the domain of $f(x)$. Also, the domain of $f(x)$ is (∞,$\frac{29}{6}$]U(5,∞).