g of g(x) = 1/ sqrt( sqrt( 1 / x+2) +2 )
which could simpify to
4throot(x+2)/ sqrt(3) if you combine the bottom into one function.
What i'm interested in is where the sqrt(3) as a denominator came from, and what happened to the two 1 values, did they cancel out.
my cousin gave me the simplified answer that he received. I proceeded to then try to solve the probem myself and could not receive the same answer he got. I actually couldn't come up with one at all. If that's the right answer i'm looking for a push in the right direction so I'll understand the thought process that's involved with this kind of question.
$\displaystyle \frac{1}{\sqrt{\sqrt{\frac{1}{x+2}+2}}}=\frac{1}{\ sqrt{\sqrt{\frac{2x+5}{x+2}}}}=\frac{1}{\left( \frac{2x+5}{x+2} \right) ^{\frac{1}{4}}}$
Assuming I understood what you typed correctly, this is how I would go about starting to simplify this. You have g(g(x)) though. Are you supposed to find g(x)?
Ok, my mistake.Originally Posted by fezz349
So it's $\displaystyle \frac{1}{\sqrt{\sqrt{\frac{1}{x+2}}+2}}$
This is equal to $\displaystyle \frac{1}{\sqrt{\frac{1}{\sqrt{x+2}}+2}}=\frac{1}{\ sqrt{\frac{2\sqrt{x+2}+1}{\sqrt{x+2}}}}$
Now apply the square root separately to the numerator and denominator and keep simplifying. That's the way I'd go about it.
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here's wat my cousin did, and tell me if it makes sense at all to you as well if you don't mind..
