Determine whether the given function is one-to-one. If it is one-to-one, find its inverse function.
-f(x)= 3x + 4
A) $f ^ { - 1 } ( x ) = \frac { x + 4 } { 3 }$
B) $\mathrm { f } ^ { - 1 } ( \mathrm { x } ) = \frac { \mathrm { x } - 4 } { 3 }$
C) $f ^ { - 1 } ( x ) = - \frac { x + 3 } { 4 }$
D)not a one-to-one function

Question

Quizplus · Accepted Answer

The function $f(x) = 3x + 4$ is one-to-one because for every x value, there is a unique y value, and it passes the horizontal line test. To find the inverse, we swap x and y and solve for y: $x = 3y + 4$, leading to $y = \frac{x - 4}{3}$, which corresponds to choice B.

Determine Whether the Given Function Is One-To-One f−1(x)=x+43f ^ { - 1 } ( x ) = \frac { x + 4 } { 3 }f−1(x)=3x+4​

Determine Whether the Given Function Is One-To-One $f ^ { - 1 } ( x ) = \frac { x + 4 } { 3 }$