Find the inverse of the function.
$$f ( x ) = \frac { 1 + 8 x } { 8 - 5 x }$$
A)$f ^ { - 1 } ( x ) = \frac { 8 x - 1 } { x + 8 }$
B)$f ^ { - 1 } ( x ) = \frac { 8 x - 1 } { 5 x + 8 }$
C)$f ^ { - 1 } ( x ) = \frac { x - 1 } { 5 x + 8 }$
D)$f ^ { - 1 } ( x ) = \frac { 8 x - 1 } { 8 x + 5 }$
E)$f ^ { - 1 } ( x ) = \frac { 5 x - 1 } { 5 x + 8 }$

Question

Quizplus · Accepted Answer

To find the inverse function, $f^{-1}(x)$, we swap $x$ and $y$ in the original function and solve for $y$. Starting with $y = \frac{1 + 8x}{8 - 5x}$, we swap to get $x = \frac{1 + 8y}{8 - 5y}$, and solve for $y$. Multiplying both sides by $8 - 5y$ and rearranging gives $y = \frac{8x - 1}{5x + 8}$, which matches choice B.

Find the Inverse of the Function f(x)=1+8x8−5xf ( x ) = \frac { 1 + 8 x } { 8 - 5 x }f(x)=8−5x1+8x​

Find the Inverse of the Function $f ( x ) = \frac { 1 + 8 x } { 8 - 5 x }$