what is the inverse of f(x) = -5x-4

Accepted Solution

Answer:[tex]\displaystyle f^{-1}(x) = -\frac{1}{5}x - \frac{4}{5}[/tex].Step-by-step explanation:The question has provided an expression for the function [tex]f(x)[/tex] and is asking for its inverse, [tex]f^{-1}(x)[/tex].Based on the definition of inverse functions, [tex]f(f^{-1}(x)) = x[/tex].Let [tex]y = f^{-1}(x)[/tex].[tex]f(y) = x[/tex].[tex]-5 y - 4= x[/tex].Solve this equation for [tex]f^{-1}(x) = y[/tex]:[tex]-5y = x +4[/tex].[tex]\displaystyle y = (-\frac{1}{5})\cdot (x + 4) = -\frac{x}{5} -\frac{4}{5}[/tex].However, [tex]f^{-1}(x)=y[/tex] As a result,[tex]\displaystyle f^{-1}(x) = -\frac{x}{5} -\frac{4}{5}[/tex].