You can put this solution on YOUR website! You may be tempted to think that , but that is not true for all 'x'. It is only true if 'x' is positive. This is where you made a mistake. You're thinking that , but with the given domain, this is not true.
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Recall that if 'x' is positive. So if . Solve for 'x' to get . Since , this means that is most certainly true and that is also true.
On the flip side, if (ie x is negative). Notice that only because means that (which is certainly true since ). So once again
To recap, and . If this makes no sense at all why these two equations hold, just graph the two functions with the domain . Let's now use this info to simplify the expression.
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Start with the given expression.
Plug in and
Negate the negative
Combine like terms.
So where
So for example, if , then and also which confirms that when . We can use other numbers in the domain to reconfirm our answer.
A better confirmation would be to graph and to see that the two graphs match up completely over the domain
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