f(x)=\frac{2}{x-1}-\frac{6}{(x-1)(2 x+1)}, \quad x>1 \text { (a) Prove that } f(x)=\frac{4}{2 x+1} (b) Find the range of f. \text { (c) Find } f^{-1}(x) (d) Find the range of f-1 on the given interval.

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