Question

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

Answer 1

Answer:

$\displaystyle f^{-1}(x) = -\frac{1}{5}x - \frac{4}{5}$.

Step-by-step explanation:

The question has provided an expression for the function $f(x)$ and is asking for its inverse, $f^{-1}(x)$.

Based on the definition of inverse functions,

$f(f^{-1}(x)) = x$.

Let $y = f^{-1}(x)$.

$f(y) = x$.

$-5 y - 4= x$.

Solve this equation for $f^{-1}(x) = y$:

$-5y = x +4$.

$\displaystyle y = (-\frac{1}{5})\cdot (x + 4) = -\frac{x}{5} -\frac{4}{5}$.

However, $f^{-1}(x)=y$ As a result,

$\displaystyle f^{-1}(x) = -\frac{x}{5} -\frac{4}{5}$.

Answer 2

Answer:

$\large\boxed{f^{-1}(x)=-\dfrac{x+4}{5}}$

Step-by-step explanation:

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