Answer:
The inverse function of \(f(x) =\frac{19}{x^3}\)
\(f(x)^{-1}=\sqrt[3]{\frac{19}{x}}\)
Step-by-step explanation:
\(f(x) = \frac{19}{x^3}\)
Steps to inverse the functions:
Step 1: x ⇔ y
\(x=\frac{19}{y^3}\)
Step 2 : now solve the equation for y:
\(y^3=\frac{19}{x}\)
\(y=\sqrt[3]{\frac{19}{x}}\)
The above equation is the inverse of the given function f(x).
\(f(x)^{-1}=\sqrt[3]{\frac{19}{x}}\)
