>> Sometimes functions are defined in parts and this kind of definition for a function is said to be piecewise or we could say that we have a split domain here that we do have a domain but it's kind of split into 2 definitions, something like that. f of x is x squared+1 if x is less than 0. So when x is negative we have this definition for the function and if x is positive or 0 we have this definition for the function. So if we're using function notation for evaluation purposes we have to decide which category we're in. f of -3 for example we would have to say well it says in the f function replace x with -3. Since x is to be replaced with a - number we have to go over here and say ok we do this if x is less than 0 and x is less than 0 here so we're gonna do that you see.
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>> So it's x squared + 1 or -3 squared + 1 and that's 9+1 or 10. Now what about f of 0? Well what category are we in? x is to be replaced with a 0 here. Where does that fall? Well it says x is greater than or equal to 0, we do this then. You see so it's x-2 and it's therefore 0-2 or simply -2. f of 5; x is positive here so we go into the category where x is to be positive and we follow this direction. It is 5-2 then in making the replacement 5-2 is 3.