Find the inverse of the one-to-one function.
-$$f ( x ) = 5 x + 7$$
A) $f ^ { - 1 } ( x ) = - \frac { x - 7 } { 5 }$
B) $f ^ { - 1 } ( x ) = \frac { x - 7 } { 5 }$
C) $\mathrm { f } ^ { - 1 } ( \mathrm { x } ) = \frac { \mathrm { x } + 7 } { 5 }$
D) $\mathrm { f } ^ { - 1 } ( \mathrm { x } ) = - \frac { \mathrm { x } + 5 } { 7 }$

Question

Quizplus · Accepted Answer

To find the inverse of the function $f(x) = 5x + 7$, you swap $x$ and $f(x)$ and solve for the new $x$. This gives $x = 5y + 7$. Solving for $y$ gives $y = \frac{x - 7}{5}$, which matches choice B.

Find the Inverse of the One-To-One Function f(x)=5x+7f ( x ) = 5 x + 7f(x)=5x+7

Find the Inverse of the One-To-One Function $f ( x ) = 5 x + 7$