Question

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

Answer 1

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

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)}\\\\(-5y)/(-5)=(x+4)/(-5)\\\\y=-(x+4)/(5)`

Answer 2

`\displaystyle f^(-1)(x) = -(1)/(5)x - (4)/(5)`.

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 = (-(1)/(5))\cdot (x + 4) = -(x)/(5) -(4)/(5)`.

However,
`f^(-1)(x)=y` As a result,

`\displaystyle f^(-1)(x) = -(x)/(5) -(4)/(5)`.