Respuesta :

jacob193

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].

gmany

Answer:

[tex]\large\boxed{f^{-1}(x)=-\dfrac{x+4}{5}}[/tex]

Step-by-step explanation:

[tex]f(x)=-5x-4\to y=-5x-4\\\\\text{Exchange x to y and vice versa:}\\\\x=-5y-4\\\\\text{Solve for}\ y:\\\\-5y-4=x\qquad\text{add 4 to both sides}\\\\-5y=x+4\qquad\text{divide both sides by (-5)}\\\\\dfrac{-5y}{-5}=\dfrac{x+4}{-5}\\\\y=-\dfrac{x+4}{5}[/tex]

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