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

Question

Quizplus · Accepted Answer

To find the inverse function, $f^{-1}(x)$, we swap $x$ and $y$ in the original function $f(x) = \frac{9}{5}x + 32$ 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.

Find a Formula for the Inverse of the Function Described 32∘32 ^ { \circ }32∘

Find a Formula for the Inverse of the Function Described $32 ^ { \circ }$