1. The problem asks to find the inverse function of \( f(x) = \frac{10}{7x^3} - 2 \) where \( x \in \mathbb{R} \). 2. To find the inverse function \( f^{-1}(x) \), we start by setting \( y = f(x) \): \[ y = \frac{10}{7x^3} - 2 \] 3. The goal is to solve for \( x \) in terms of \( y \). First, isolate the fraction term: \[ y + 2 = \frac{10}{7x^3} \] 4. Next, take the reciprocal of both sides: \[ \frac{1}{y + 2} = \frac{7x^3}{10} \] 5. Multiply both sides by \( \frac{10}{7} \) to isolate \( x^3 \): \[ x^3 = \frac{10}{7(y + 2)} \] 6. Finally, take the cube root of both sides to solve for \( x \): \[ x = \sqrt[3]{\frac{10}{7(y + 2)}} \] 7. Replace \( y \) with \( x \) to write the inverse function: \[ f^{-1}(x) = \sqrt[3]{\frac{10}{7(x + 2)}} \] This is the inverse function of \( f(x) \).