My Math Forum What method can be used to work with embedded functions as shown in this problem?

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November 8th, 2018, 04:15 PM   #11
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Quote:
 Originally Posted by Chemist116 Sorry I wasn't aware of that. But from looking at the messages it looks that $x=\frac{11}{12}$. But does it means that there are other solutions as well?. I missed this part. Which would be the other solution?.
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November 8th, 2018, 05:06 PM   #12
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Quote:
 Originally Posted by Chemist116 $\phi^{-1}\left(\phi\left( 2x+1\right)\right)=\phi^{-1}\left(6x-10\right)$ $2x+1= \frac{y+10}{6}$
That isn't a correct way to obtain the inverse. If you look carefully at what you did, you may be able to see why.

Once you have the correct inverse, namely $\phi^{-1}(x) = (x + 13)/3$,
applying it to the second equation gives $f(x) - 3 = ((3x - 4) + 13)/3 = x + 3$, so $f(x) = x + 6$.

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