I need help finding an inverse of a function: f(x) = -2 sqrt[2x + 4] - 5

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barcacookie

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The question was
29547428_1955367061154380_2053687307_n.png



The answer I got was
1


My work is attached.

Was I correct and how would I be able to check?
 

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barcacookie said:
The question was
29547428_1955367061154380_2053687307_n.png



The answer I got was
1


My work is attached.

Was I correct and how would I be able to check?
Click to expand...

That looks correct. You didn't make any of the usual mistakes (unless I did, too).

I would do two things to check it. First, simplify f(f-1(x)) and confirm that it is x (watching the domain and range as you do this). Second, sketch the graph of each function (taking domain and range into account), and see that they are reflections of one another in the line y=x.
 
Also, I was wondering why the range was less than or equal to -5 and not but not greater than or equal to? Was it because of a reflection with respect to the x-axis?
 
Also, when trying to check my work by doing the method you told me, I am having trouble trying to find if f(f-1(x)) = x 29633771_1955421331148953_807648209_o.jpg

I am lost in the algebra
 
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