Answer:
[tex]{f}^{ - 1} (x)= \frac{ 5 - 2x }{ 4x + 1}[/tex]
Step-by-step explanation:
The given rational function is
[tex]f(x) = \frac{x - 5}{ - 4x - 2} [/tex]
Let
[tex]y = \frac{x - 5}{ - 4x - 2} [/tex]
Interchange x and y
[tex]x= \frac{y- 5}{ - 4y - 2} [/tex]
Cross multiply
[tex]x( - 4y - 2)= y- 5 [/tex]
Expand
[tex]- 4xy - 2x= y- 5 \\ - 4xy - y= 2x - 5 \\y( - 4x - 1)= 2x - 5[/tex]
Solve for y;
[tex]y= \frac{ 2x - 5}{ - 4x - 1} [/tex]
or
[tex]y= \frac{ 5 - 2x }{ 4x + 1} [/tex]
Therefore
[tex] {f}^{ - 1} (x)= \frac{ 5 - 2x }{ 4x + 1} [/tex]
