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Find two functions f(x) and g(x) such that f(g(x)) = x but g(f(x)) does not = x.?
I had trouble with this as well, but with a few hints from my teacher, I eventually figured it out.
Using square roots and negatives, I came up with these two equations:
Note that both equations have a negative in the front. When you plug these into f(g(x)) and g(f(x)), you get:
f(g(x))=-(-(sqrt(x))^2 …………………The square root and square cancel out, leaving:
=-(-x) ………………….which simplifies to:
Now for g(f(x)):
g(f(x))=-(sqrt(-(x^2))) …………………This doesn t simplify anymore than this since whatever
you square for x will end up being negative anyway.
Even though the original post was quite a while ago, I hope this helps anyone in the future!
Source(s): Hints from my teacher and my brain slowly, but eventually, piecing it together.
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