$32 ^ { \circ }$ Fahrenheit = $0 ^ { \circ }$ Celsius. A function that converts temperatures in Celsius to those in Fahrenheit is $f ( x ) = \frac { 9 } { 5 } x + 32$ Fahrenheit. Find a formula for the inverse of this function.
A) $f ^ { - 1 } ( x ) = x + 32$
B) $f ^ { - 1 } ( x ) = \frac { 5 } { 9 } ( x - 32 )$
C) $f ^ { - 1 } ( x ) = \frac { 5 } { 9 } ( x + 32 )$
D) $f ^ { - 1 } ( x ) = \frac { 9 } { 5 } x + 32$

Question

$32 ^ { \circ }$ Fahrenheit  = $0 ^ { \circ }$ Celsius. A function that converts temperatures in Celsius to those in Fahrenheit is $f ( x ) = \frac { 9 } { 5 } x + 32$ Fahrenheit. Find a formula for the inverse of this function.
A) $f ^ { - 1 } ( x ) = x + 32$
B) $f ^ { - 1 } ( x ) = \frac { 5 } { 9 } ( x - 32 )$
C) $f ^ { - 1 } ( x ) = \frac { 5 } { 9 } ( x + 32 )$
D) $f ^ { - 1 } ( x ) = \frac { 9 } { 5 } x + 32$

Quizplus · Accepted Answer

To find the inverse function, $f^{-1}(x)$, we swap $x$ and $y$ in the original function $y = \frac{9}{5}x + 32$ and solve for $y$. This gives $x = \frac{9}{5}y + 32$, which when solved for $y$, gives $y = \frac{5}{9}(x - 32)$, corresponding to choice B.

32∘32 ^ { \circ }32∘ Fahrenheit = 0∘0 ^ { \circ }0∘

$32 ^ { \circ }$ Fahrenheit = $0 ^ { \circ }$