Find the inverse of the function.
-$$f ( x ) = \frac { 7 } { x + 7 }$$
A) $\mathrm { f } ^ { - 1 } ( \mathrm { x } ) = \frac { - 7 \mathrm { x } + 7 } { \mathrm { x } }$
B) $\mathrm { f } ^ { - 1 } ( \mathrm { x } ) = \frac { 7 + 7 \mathrm { x } } { \mathrm { x } }$
C) $\mathrm { f } ^ { - 1 } ( \mathrm { x } ) = \frac { \mathrm { x } } { 7 + 7 \mathrm { x } }$
D) Not a one-to-one function

Question

Quizplus · Accepted Answer

To find the inverse of the function $f(x) = \frac{7}{x + 7}$, you swap $x$ and $y$ and solve for $y$. So, $x = \frac{7}{y + 7}$. Multiplying both sides by $y + 7$ and then by $x$ gives $xy + 7x = 7$. Solving for $y$ gives $y = \frac{7 - 7x}{x}$, which matches choice A.

Find the Inverse of the Function f(x)=7x+7f ( x ) = \frac { 7 } { x + 7 }f(x)=x+77​

Find the Inverse of the Function $f ( x ) = \frac { 7 } { x + 7 }$