1. Consider the function defined as \(f(x) = \displaystyle{\frac{x^3-2}{5}}\).
   1. Convince yourself this function is invertible.
   2. Write down a formula for \(\frac{\mathrm{d}}{\mathrm{d}x}f^{-1}(x)\) using the inverse function theorem.
   3. Now Write down a formula for \(\frac{\mathrm{d}}{\mathrm{d}x}f^{-1}(x)\) by first finding a formula for \(f^{-1}(x)\), then taking a derivative. Convince yourself it’s the same formula as the one you got using the inverse function theorem.
2. Similarly, calculate a formula for the derivative of the inverse of this function two different ways: \[g(x) = \frac{3}{\sqrt[5]{x}-1}\]