Determine whether the function is one-to-one. If it is one-to-one find an equation or a set of ordered pairs that defines
the inverse function of the given function.
-$f ( x ) = 3 - 2 x$
A) one-to-one; $\mathrm { f } ^ { - 1 } ( \mathrm { x } ) = \frac { - \mathrm { x } + 3 } { 2 }$
B) one-to-one; $\mathrm { f } ^ { - 1 } ( \mathrm { x } ) = \frac { 1 } { 3 - 2 \mathrm { x } }$
C) one-to-one; $\mathrm { f } ^ { - 1 } ( \mathrm { x } ) = \frac { \mathrm { x } - 3 } { 2 }$
D) not one-to-one

Question

Quizplus · Accepted Answer

The function $f(x) = 3 - 2x$ is one-to-one because for each input $x$, there is a unique output, and it passes the horizontal line test. To find the inverse, swap $x$ and $y$ and solve for $y$: $x = 3 - 2y$, leading to $y = \frac{-x + 3}{2}$, which matches choice A.

Determine Whether the Function Is One-To-One f(x)=3−2xf ( x ) = 3 - 2 xf(x)=3−2x

Determine Whether the Function Is One-To-One $f ( x ) = 3 - 2 x$