Question

find the inverse function of the function $f(x) = \frac{4}{9x}$.
answer attempt 1 out of 2
$\circ$ $f^{-1}(x) = -\frac{9}{4x}$
$\circ$ $f^{-1}(x) = \frac{9}{4x}$
$\circ$ $f^{-1}(x) = -\frac{4}{9x}$
$\circ$ $f^{-1}(x) = \frac{4}{9x}$

Explanation:

Step1: Set $y = f(x)$

$y = \frac{4}{9x}$

Step2: Swap $x$ and $y$

$x = \frac{4}{9y}$

Step3: Solve for $y$

Multiply both sides by $9y$: $9xy = 4$
Divide both sides by $9x$: $y = \frac{4}{9x}$

Answer:

$f^{-1}(x) = \frac{4}{9x}$