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.
-$$f ( x ) = 5 - 4 x$$
A) one-to-one; $\mathrm { f } ^ { - 1 } ( \mathrm { x } ) = \frac { 1 } { 5 - 4 \mathrm { x } }$
B) one-to-one; $\mathrm { f } ^ { - 1 } ( \mathrm { x } ) = \frac { - \mathrm { x } + 5 } { 4 }$
C) one-to-one; $\mathrm { f } ^ { - 1 } ( \mathrm { x } ) = \frac { \mathrm { x } - 5 } { 4 }$
D) not one-to-one

Question

Quizplus · Accepted Answer

The function $f(x) = 5 - 4x$ is one-to-one because for each input $x$, there is exactly one output $y$, and it passes the horizontal line test. To find the inverse, we swap $x$ and $y$ and solve for $y$: $x = 5 - 4y$, leading to $y = \frac{-x + 5}{4}$, which matches choice B.

Determine Whether the Function Is One-To-One f(x)=5−4xf ( x ) = 5 - 4 xf(x)=5−4x

Determine Whether the Function Is One-To-One $f ( x ) = 5 - 4 x$