Question

question
for the function $f(x) = \frac{3x+10}{4-5x}$, find $f^{-1}(x)$.
answer attempt 1 out of 3
$f^{-1}(x) = $

Explanation:

Step1: Set $y=f(x)$

$y = \frac{3x+10}{4-5x}$

Step2: Swap $x$ and $y$

$x = \frac{3y+10}{4-5y}$

Step3: Cross-multiply to eliminate fraction

$x(4-5y) = 3y+10$

Step4: Expand left-hand side

$4x - 5xy = 3y + 10$

Step5: Group terms with $y$

$4x - 10 = 3y + 5xy$

Step6: Factor out $y$ on right

$4x - 10 = y(3 + 5x)$

Step7: Solve for $y$

$y = \frac{4x - 10}{5x + 3}$

Answer:

$f^{-1}(x)=\frac{4x-10}{5x+3}$