Find the roots of this function:

[Soup674]

[math]f(x)=(x-2)^2-4|x-2|-1[/math]I understand how absolute value functions work on their own but within a function I'm not sure how to solve for y=0, I've tried 2 different methods and each gives me one of the solutions plus another value that is not correct.

 

[mmm4444bot]

Hello. Please share one of your attempts.

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[Steven G]

You need to understand absolutes to work out this problems.

Sometimes |x-2| = x-2. What are the conditions for this?
Other times |x-2| = -(x-2) = 2-x. What are the conditions for this?
If you can answer the above questions then you should be able to solve your problems.

If you want help then it would be advisable for you to post your work so we can see where you are wrong and then help you correct that mistake

 

[Dr.Peterson]

[math]f(x)=(x-2)^2-4|x-2|-1[/math]I understand how absolute value functions work on their own but within a function I'm not sure how to solve for y=0, I've tried 2 different methods and each gives me one of the solutions plus another value that is not correct.

It may be your work, rather than the method, that gives invalid answers!

I myself would start by letting u = |x-2| and solving for u.