For the given function f(x), find f-1(x).
-$$f ( x ) = \frac { x - 10 } { x - 6 }$$
A) $f ^ { - 1 } ( x ) = \frac { x + 10 } { - 6 + x }$
B) $f ^ { - 1 } ( x ) = \frac { 6 x - 1 } { x - 10 }$
C) $f ^ { - 1 } ( x ) = \frac { - 6 x - 10 } { x - 1 }$
D) $\mathrm { f } ^ { - 1 } ( \mathrm { x } ) = \frac { 6 \mathrm { x } - 10 } { \mathrm { x } - 1 }$

Question

Quizplus · Accepted Answer

To find the inverse function, we first replace f(x) with y and then solve for x.

$$y=\frac{x-10}{x-6}$$

$$xy-6y=x-10$$

$$xy-x=6y-10$$

$$x(y-1)=6y-10$$

$$x=\frac{6y-10}{y-1}$$

Thus, the inverse function is

$$f^{-1}(x)=\frac{6x-10}{x-1}$$

Therefore, the correct answer is D.

For the Given Function F(x), Find F-1(x) f(x)=x−10x−6f ( x ) = \frac { x - 10 } { x - 6 }f(x)=x−6x−10​

For the Given Function F(x), Find F-1(x) $f ( x ) = \frac { x - 10 } { x - 6 }$