SOLUTION: Hi there, I've been trying and trying this problem with no luck. Could you help me out with this, please? Given the function y=(x-11)^2, where x is less than or equal to 11, fi

Question 921397: Hi there, I've been trying and trying this problem with no luck. Could you help me out with this, please?
Given the function y=(x-11)^2, where x is less than or equal to 11, find the inverse and its domain.
I keep getting y=plus or minus sqrt(x)-1 which is incorrect.

Found 2 solutions by josgarithmetic, jim_thompson5910:
Answer by josgarithmetic(39617) (Show Source): You can put this solution on YOUR website!
Domain of given y is and range is .

The inverse h(x) of this y has domain and range .

FINDING THE INVERSE, h(x):
, vertical and horizontal components change places.

---And again, be reminded of the domain and the range. You need to use the MINUS square root form and reject the other branch.
Answer by jim_thompson5910(35256) (Show Source): You can put this solution on YOUR website!
The domain of the original function is . This is given to you and this restriction is made to force f(x) to be one-to-one.

The range of the original function is . This is found either through the graph or by knowing that (x-11)^2 is either 0 or positive. You can't square a number and get something negative.

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When you solve for the inverse, you swap x and y and solve for y. Doing that also swaps the domain and range. Why? Because the domain is simply the set of allowed x values (inputs) and the range is the set of possible y values (outputs).

Again, the domain and range swap. This is important.

So the inverse will have the domain of and the range of

The range for the inverse is what is important here.

When you swap x and y, then solve for y, you should get this:

But keep in mind that the range of the inverse is . This means negative y values such as are possible in the range of the inverse.

This is only possible if you pick the negative square root. You cannot generate negative y values with . It's impossible. The two pieces are always positive.

So the inverse is

You can rewrite that as

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Let me know if that helps or not. Thanks.

If you need more help, feel free to email me at jim_thompson5910@hotmail.com

My Website: http://www.freewebs.com/jimthompson5910/home.html

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