Determine whether the given function is one-to-one. If it is one-to-one, find its inverse function.
-$$f ( x ) = \frac { 2 } { x }$$
A) $f ^ { - 1 } ( x ) = \frac { x } { 2 }$
B) $\mathrm { f } ^ { - 1 } ( \mathrm { x } ) = \frac { 2 } { \mathrm { x } }$
C) $\mathrm { f } ^ { - 1 } ( \mathrm { x } ) = - 2 \mathrm { x }$
D)not a one-to-one function

Question

Quizplus · Accepted Answer

The function $f(x) = \frac{2}{x}$ is one-to-one because for every unique x-value, there is a unique y-value, and it passes the horizontal line test. To find the inverse, swap x and y and solve for y: $x = \frac{2}{y}$, leading to $y = \frac{2}{x}$, which is option B.

Determine Whether the Given Function Is One-To-One f(x)=2xf ( x ) = \frac { 2 } { x }f(x)=x2​

Determine Whether the Given Function Is One-To-One $f ( x ) = \frac { 2 } { x }$