Question

which function is the inverse of ( f(x) = -5x - 4 )?
( f^{-1}(x) = -\frac{1}{5}x - \frac{4}{5} )
( f^{-1}(x) = -\frac{1}{5}x + \frac{4}{5} )
( f^{-1}(x) = -4x + 5 )
( f^{-1}(x) = 4x + 4 )

Explanation:

Step1: Set $y=f(x)$

$y = -5x - 4$

Step2: Swap $x$ and $y$

$x = -5y - 4$

Step3: Solve for $y$

Add 4 to both sides: $x + 4 = -5y$
Divide by -5: $y = -\frac{1}{5}x - \frac{4}{5}$

Answer:

$\boldsymbol{f^{-1}(x) = -\frac{1}{5}x - \frac{4}{5}}$ (corresponding to the first option)