Problem 387 (difficulty: 2/10)

Show that the following functions are injective on the given set \(\displaystyle H\), and calculate the inverse.

 (1)  \(\displaystyle f(x)=\frac{x}{x+1}, \ H=[-1,1]\);     (2)  \(\displaystyle f(x)=\frac{x}{|x|+1}, \ H=\R.\)

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