Final answer:
The inverse function of f(x) = -5x - 4 is f⁻¹(x) = -(y + 4) / 5.
Step-by-step explanation:
The inverse of a function can be found by swapping the x and y variables and solving for y. To find the inverse of the function f(x) = -5x - 4, we can rewrite it as y = -5x - 4. Swap the x and y variables to get x = -5y - 4.
Now, solve for y by isolating it on one side of the equation:
y = -5x - 4
To isolate x, use the following steps:
Add 4 to both sides of the equation:
y + 4 = -5x
Divide both sides of the equation by -5:
(y + 4) / -5 = x
Simplify:
x = -(y + 4) / 5
Therefore, the inverse of f(x) = -5x - 4 is f⁻¹(x) = -(y + 4) / 5.