I'm not sure what exactly the function will look like, because it depends on where the brackets are. There are three possibilities, so I'll explain each of them.
Option 1: f(x) = √(x 2) - 1
This function looks like it should be the same as f(x) = x-1. After all, taking a square root should just undo the square, right? But when we see this, we have to remember that this implies only the positive square root! For example, 1^2 and (-1)^2 are both 1, but √1 is always assumed to mean 1. So both √(5^2) and √(-5^2) are assumed to be 5. This means that the graph of this function will actually look like a wide V, with the corner at (0,-1).
Option 2: f(x) = (√x) 2 - 1
Depending on how good your calculator is, this may result in half of what you'd expect. It is commonly assumed that the square root of a negative number doesn't exist, so this function might look like f(x) = x-1 for all positive values of x (and zero). However, this graph should technically look exactly like f(x) = x-1, because while the square root of a negative number certainly wouldn't show up on a graph, it does technically exist. These are called imaginary numbers, and while I won't get into too much detail, in this case, the square and square root actually would simply reverse each other. Basically, this demonstrates that with certain functions, order matters, and while a square root doesn't just undo a square, a square does undo a square root.
Option 3: f(x) = √(x 2 - 1)
I think this is the least likely option of the three, but for completeness' sake, I'm throwing it in anyway. It's also the most interesting looking graph. What happens is an odd combination of the quirks of the first two options. If you set x as any number in between 1 and -1, then x 2-1 is negative, and so its square root doesn't exist. This leaves the rest of the graph, which still looks a lot like the first option, but curves downward to approach f(x) = 0 a lot more quickly towards the end. It looks a bit like a funnel, and if you take a step back and look at a big enough area on the graph that the gap at the bottom is too small to see, it looks exactly the same as the first one.
Anyway, pick a graph, and always remember to include your brackets. They're important!
