Question

inverse of rational functions
score: 0/2 penalty: none
question
for the function $f(x) = \frac{4x-9}{2x}$, find $f^{-1}(x)$.
answer attempt 1 out of 3
$f^{-1}(x) = $

Explanation:

Step1: Set $y = f(x)$

$y = \frac{4x - 9}{2x}$

Step2: Swap $x$ and $y$

$x = \frac{4y - 9}{2y}$

Step3: Cross-multiply to eliminate denominator

$x \cdot 2y = 4y - 9$
$2xy = 4y - 9$

Step4: Isolate terms with $y$

$2xy - 4y = -9$
$y(2x - 4) = -9$

Step5: Solve for $y$

$y = \frac{-9}{2x - 4} = \frac{9}{4 - 2x}$

Answer:

$\frac{9}{4 - 2x}$