Determine whether the given function is one-to-one. If it is one-to-one, find a formula for the inverse.
-$$f ( x ) = \frac { 2 } { x + 3 }$$
A) $f ^ { - 1 } ( x ) = \frac { - 3 x + 2 } { x }$
B) $f ^ { - 1 } ( x ) = \frac { x } { 3 + 2 x }$
C) $f ^ { - 1 } ( x ) = \frac { 3 + 2 x } { x }$
D) Not one-to-one

Question

Quizplus · Accepted Answer

To determine if $f(x) = \frac{2}{x+3}$ is one-to-one, we check if each output corresponds to exactly one input. This function is one-to-one because for any two different values of $x$, the function yields two different outputs. To find the inverse, we swap $x$ and $y$ and solve for $y$: $x = \frac{2}{y+3}$. Solving for $y$, we get $y = \frac{2 - 3x}{x}$, which matches choice A.

Determine Whether the Given Function Is One-To-One f(x)=2x+3f ( x ) = \frac { 2 } { x + 3 }f(x)=x+32​

Determine Whether the Given Function Is One-To-One $f ( x ) = \frac { 2 } { x + 3 }$