Question

Determine the domain and range of the function f(x) = Vx – 4. Enter your answersin interval notation.

Answer 1

The domain of a function is the group of numbers that can be used as an input, while the range is the group of numbers that can be the output of the function.

For this case, the domain is constrained, because the "x" value is inside a square root, there is no real values for negative square roots, so the argument of this can't be negative, therefore:

`\begin{gathered} x-4\ge0 \\ x\ge4 \end{gathered}`

While the output can be all non-negative real numbers, because at the lowest possible value the argument of the square root will be 0. Therefore we have:

`\begin{gathered} \text{Domain: }x\ge4 \\ \text{Range: }y\ge0 \end{gathered}`