Question

find the inverse function of the function $f(x) = -\frac{9x}{5}$. answer attempt 1 out of 2 $f^{-1}(x) = \frac{5x}{9}$ $f^{-1}(x) = \frac{5}{9x}$ $f^{-1}(x) = -\frac{5x}{9}$ $f^{-1}(x) = -\frac{5}{9x}$

Explanation:

Step1: Set $y = f(x)$

$y = -\frac{9x}{5}$

Step2: Swap $x$ and $y$

$x = -\frac{9y}{5}$

Step3: Solve for $y$

Multiply both sides by 5: $5x = -9y$
Divide by $-9$: $y = -\frac{5x}{9}$

Step4: Replace $y$ with $f^{-1}(x)$

$f^{-1}(x) = -\frac{5x}{9}$

Answer:

$f^{-1}(x) = -\frac{5x}{9}$