Answer
(a) $g^{-1}(C)=\frac{5(C-32)}{9}$
The inverse represents Celsius value for given Fahrenheit.
(b) $g^{-1}(86)=30$
It represents amount of Celsius for given Fahrenheit.
Work Step by Step
$g(C)=\frac{9}{5}C+32$
(a) To find the inverse of this function, we will follow the next steps:
First write the function in terms of $y$ and $C$.
$y=\frac{9}{5}C+32$
Then replace $y$ by $C$ and vice versa:
$C=\frac{9}{5}y+32$
And solve it for $y$:
$\frac{9}{5}y=C-32$
$y=\frac{5(C-32)}{9}$
$g^{-1}(C)=\frac{5(C-32)}{9}$
The inverse represents Celsius value for given Fahrenheit.
(b)
$g^{-1}(86)=\frac{5(86-32)}{9}=\frac{5\times54}{9}=30$
It represents amount of Celsius for given Fahrenheit. Which means that $86$ by Fahrenheit is $30$ Celsius.
