Question

What is the domain of this function? f(x)=3√x-2

Answer 1

$Domain:\lbrack2,\infty)$

Explanation

The domain of a function is the complete set of possible values of the independent variable,

Step 1

given

$f(x)=3\sqrt{x-2}$

The domain of a radical function is any x value for which the radicand (the value under the radical sign) is not negative Since the square root must always be positive or 0,

so,let's solve for x

$\begin{gathered} x-2\ge0 \\ add\text{ 2 in both sides} \\ x-2+2\geqslant0+2 \\ x\ge2 \end{gathered}$

so, the domain is all numbers equal or greater than 2

$Domain:\lbrack2,\infty)$

I hope this helps you