Question

What is the domain of the function

Answer 1

Answer:

$x\geq -6$

Step-by-step explanation:

The domain of a function is all of the values that $x$ can be under that specific function. In this case, we're asking what values of $x$ allow $\sqrt{\frac{1}{3} x+2}$ to exist.

In order for square roots to exist, the quantity under the square root must be greater than or equal to $0$, because you can't take the square root of a negative number. Therefore, we can write the following inequality to solve for $x$:

$\frac{1}{3}x+2\geq 0$

Solving this inequality, we get:

$\frac{1}{3}x+2\geq 0$

$\frac{1}{3}x\geq -2$ (Subtract $2$ from both sides of the inequality to isolate $x$)

$x\geq -6$ (Multiply both sides of the inequality by $3$ to get rid of $x$'s coefficient)

Hope this helps!