The function f is one-to-one. Find its inverse.
-$$f ( x ) = \frac { 4 } { 7 x - 5 }$$
A) $f ^ { - 1 } ( x ) = \frac { 4 + 5 x } { 7 x }$

B) $f ^ { - 1 } ( x ) = \frac { - 5 x - 4 } { 7 x }$

C) $f ^ { - 1 } ( x ) = \frac { 7 x - 5 } { 4 }$

D) $\mathrm { f } ^ { - 1 } ( x ) = \frac { 4 + 5 y } { 7 y }$

Question

The function f is one-to-one. Find its inverse.
-$$f ( x ) = \frac { 4 } { 7 x - 5 }$$
A) $f ^ { - 1 } ( x ) = \frac { 4 + 5 x } { 7 x }$

B) $f ^ { - 1 } ( x ) = \frac { - 5 x - 4 } { 7 x }$

C) $f ^ { - 1 } ( x ) = \frac { 7 x - 5 } { 4 }$

D) $\mathrm { f } ^ { - 1 } ( x ) = \frac { 4 + 5 y } { 7 y }$

Quizplus · Accepted Answer

To find the inverse of a function, we need to switch the roles of x and y and solve for y.$f ( x ) = \frac { 4 } { 7 x - 5 }$$y = \frac { 4 } { 7 x - 5 }$$x = \frac { 4 } { 7 y - 5 }$$7 y - 5 = \frac { 4 } { x }$$7 y = \frac { 4 } { x } + 5$$y = \frac { 4 + 5 x } { 7 x }$Therefore, the inverse of f is $f ^ { - 1 } ( x ) = \frac { 4 + 5 x } { 7 x }$.

The Function F Is One-To-One f(x)=47x−5f ( x ) = \frac { 4 } { 7 x - 5 }f(x)=7x−54​

The Function F Is One-To-One $f ( x ) = \frac { 4 } { 7 x - 5 }$