Given:
[tex]f(x)=-\frac{3}{8}x^7[/tex]Find: the inverse of a function.
Explanation: the function is
[tex]\begin{gathered} f(x)=-\frac{3}{8}x^7 \\ y=-\frac{3}{8}x^7 \\ x=-\frac{3}{8}y^7 \\ -\frac{8}{3}x=y^7 \\ y=(-\frac{8}{3}x)^{\frac{1}{7}} \end{gathered}[/tex]Final answer: the required answer is
[tex]f^{-1}(x)=(-\frac{8}{3}x^{)\frac{1}{7}}[/tex]