Question

PROBLEM SOLVING At the start of a dog sled race

in Anchorage, Alaska, the temperature was 5°C. By
the end of the race, the
temperature was -10°C.
The formula for converting
from degrees
temperatures
Fahrenheit F to degrees
Celsius Cis C = (F - 32).
a. Find the inverse function.
Describe what it represents.
31
b. Find the Fahrenheit temperatures at the start and
end of the race.
c. Use a graphing calculator to graph the original
function and its inverse. Find the temperature that
is the same on both temperature scales.

Answer 1

a. The inverse function is
`\(F = (9)/(5)C + 32\)`. It represents the conversion from Celsius to Fahrenheit. b. At the start of the race, the Fahrenheit temperature was 41°F, and at the end, it was 14°F. c. When graphing the original function
`\(C = (5)/(9)(F-32)\)` and its inverse
`\(F = (9)/(5)C + 32\)`, the point of intersection represents a temperature that is the same on both Celsius and Fahrenheit scales. It is 5 degrees.

a. To find the inverse function, swap the roles of C and F in the formula and solve for F:
`\[ F = (9)/(5)C + 32 \]`

This represents the conversion from Celsius to Fahrenheit.

b. At the start of the race C = 5°C, the Fahrenheit temperature is
`\(F = (9)/(5)(5) + 32 = 41^\circ F\)`.

At the end of the race C = -10°C, the Fahrenheit temperature is
`\(F = (9)/(5)(-10) + 32 = 14 ^\circ F\)`.

c. Using a graphing calculator, graph both the original function
`\(C = (5)/(9)(F-32)\)` and its inverse
`\(F = (9)/(5)C + 32\)`. The point of intersection on the graph represents a temperature that is the same in both Celsius and Fahrenheit scales. It is 5 degrees.