Answer
(a) $F = (9/5) \cdot C + 32$
(b) In words, the inverse function tells us how to convert a temperature from Fahrenheit (F) to Celsius (C). Given a temperature in Fahrenheit, we can use the formula $C = (5/9) \cdot (F - 32)$ to find the equivalent temperature in Celsius.
(c) The domain of the inverse function is all real numbers and the range of the inverse function is also all real numbers.
Work Step by Step
(a) To find the inverse function, we can start with the formula $F = (9/5) \cdot C + 32$
solve for C in terms of F:
$C = (5/9) \cdot (F - 32)$
So, the inverse function is $C = (5/9) \cdot (F - 32)$, which converts Fahrenheit (F) to Celsius (C).
(b) In words, the inverse function tells us how to convert a temperature from Fahrenheit (F) to Celsius (C). Given a temperature in Fahrenheit, we can use the formula $C = (5/9) \cdot (F - 32)$ to find the equivalent temperature in Celsius.
(c)
Domain of the Inverse Function (Fahrenheit to Celsius):
The formula $C = (5/9) \cdot (F - 32)$ is valid for any real number value of F because it's a linear equation. Therefore, the domain of the inverse function is all real numbers.
Range of the Inverse Function (Fahrenheit to Celsius):
The Celsius temperature can be any real number value, so the range of the inverse function is also all real numbers.
