The function f is one-to-one. Find its inverse.
-$$f ( x ) = 3 x + 4$$
A) $f ^ { - 1 } ( x ) = \frac { x + 4 } { 3 }$

B) $f ^ { - 1 } ( x ) = \frac { x - 4 } { 3 }$

C) $f ^ { - 1 } ( x ) = \frac { x } { 3 } + 4$

D) $\mathrm { f } ^ { - 1 } ( \mathrm { x } ) = \frac { \mathrm { x } } { 3 } - 4$

Question

The function f is one-to-one. Find its inverse.
-$$f ( x ) = 3 x + 4$$
A) $f ^ { - 1 } ( x ) = \frac { x + 4 } { 3 }$

B) $f ^ { - 1 } ( x ) = \frac { x - 4 } { 3 }$

C) $f ^ { - 1 } ( x ) = \frac { x } { 3 } + 4$

D) $\mathrm { f } ^ { - 1 } ( \mathrm { x } ) = \frac { \mathrm { x } } { 3 } - 4$

Quizplus · Accepted Answer

To find the inverse of the function $f(x) = 3x + 4$, you solve for $x$ in terms of $y$, then swap $x$ and $y$. Starting with $y = 3x + 4$, solving for $x$ gives $x = \frac{y - 4}{3}$. Then, replacing $y$ with $f^{-1}(x)$ gives $f^{-1}(x) = \frac{x - 4}{3}$.

The Function F Is One-To-One f(x)=3x+4f ( x ) = 3 x + 4f(x)=3x+4

The Function F Is One-To-One $f ( x ) = 3 x + 4$