Question

What is the range of the function `x + sqrt( x-1 )`?

Answer 1

Range of function: 1 ≤ x

Explanation:

In order to determine the range of a function, you look at the complex part of that function, in this case: `sqrt(x-1)`

You must start with this, because it is always the most complex part of an function that limits it.

We know for fact that any square root cannot be negative. In other words, it must always be equal or greater than 0.

0 ≤ `sqrt(x-1)`
0 ≤ `x-1`
1 ≤ x

The above tells us that x from the given function must always be greater or equal to 1. If it is smaller than 1, then the square root would be positive, and that is impossible.

Now, you can insert any x value greater or equal to 1, and the function would work out. This means that this function only has a lower limit of 1, and there are no upper limits.