Given that f(x)=x−1+1+x−1x−1, what is f(f(−2))? Express your answer as a common fraction.
Solution — click to reveal
We have f(x)=x−1+1+x−1x−1=x1+1+x11/x. Therefore, we have f(−2)=−21+1+−21−21=−21+1−21−1/2=−21+1/2−1/2=−21−1=−23. So, we have f(f(−2))=f(−3/2)=−3/21+1+−3/211/(−3/2)=−32+1−32−2/3=−32+1/3−2/3=−32−2=−38.