Question

What is the domain of the function y=2√x-6

Answer 1

Answer

Domain of the function:

In interval notation: [6, ∞)

In set notation: {x: x∈R, x≥6}

Explanation

Remember that the the domain of the square root function are all the $x$ values such is is bigger than zero. We can express the later in set notation: {x: x∈R, x≥0}, or in interval notation: [0, ∞)

This is because the square root is not defined, in the real numbers, for negative values.

So, to find the domain of our function, we just need to set the thing inside the radical grater or equal than zero and solve for x:

$x-6\geq 0$

$x\geq 6$

The domain of the function is all the numbers bigger than 6, including 6.

Answer 2

The domain would be [6,infinity)