The formula for converting from Celsius to Fahrenheit temperatures is F = (9/5)C + 32.
1. What is the inverse of this formula?
2. Is the inverse a function?
3. What is the Celsius temperature that corresponds to 27°F?

Formula for converting Celsius to Fahrenheit:
The formula for converting from Celsius (C) to Fahrenheit (F) is:
F=95C+32F = \frac{9}{5}C + 32
Finding the inverse of this formula:
To find the inverse, we need to solve for CC in terms of FF.
Start with the original equation:
F=95C+32F = \frac{9}{5}C + 32
Step 1: Subtract 32 from both sides:
F−32=95CF - 32 = \frac{9}{5}C
Step 2: Multiply both sides by 5 to eliminate the denominator:
5(F−32)=9C5(F - 32) = 9C
Step 3: Divide both sides by 9 to isolate CC:
C=59(F−32)C = \frac{5}{9}(F - 32)
Thus, the inverse formula is:
C=59(F−32)C = \frac{5}{9}(F - 32)
Is the inverse a function?
Yes, the inverse formula is a function. A function is defined as a relation in which each input corresponds to exactly one output. In this case, for any given Fahrenheit temperature FF, there is exactly one corresponding Celsius temperature CC, so the inverse is indeed a function.
Celsius temperature corresponding to 27∘27^\circF:
Now, let's find the Celsius temperature that corresponds to 27∘27^\circF using the inverse formula:
C=59(27−32)C = \frac{5}{9}(27 - 32)
Step 1: Subtract 32 from 27:
C=59(−5)C = \frac{5}{9}(-5)
Step 2: Multiply 59\frac{5}{9} by −5-5:
C=−259C = -\frac{25}{9}
Step 3: Simplify the fraction:
C≈−2.78∘CC \approx -2.78^\circ C
Thus, the Celsius temperature that corresponds to 27∘27^\circF is approximately −2.78∘C-2.78^\circ C.