Question

the formula for converting from celsius to fahrenheit temperatures is $f = \frac{9}{5}c + 32$. a. find the inverse of the formula. is the inverse a function?

Explanation:

Step1: Start with the formula \( F = \frac{9}{5}C + 32 \)

We need to solve for \( C \) in terms of \( F \). First, subtract 32 from both sides:
\( F - 32 = \frac{9}{5}C \)

Step2: Multiply both sides by \( \frac{5}{9} \)

To isolate \( C \), we multiply both sides by the reciprocal of \( \frac{9}{5} \), which is \( \frac{5}{9} \):
\( C = \frac{5}{9}(F - 32) \)
This is the inverse formula, converting Fahrenheit to Celsius. To check if it's a function, we use the vertical line test (or the definition: for each input \( F \), there is exactly one output \( C \)). Since it's a linear function (degree 1), and linear functions (except vertical lines) are functions, this inverse is a function.

Answer:

The inverse formula is \( C = \frac{5}{9}(F - 32) \), and yes, the inverse is a function.