Question

The formula to convert a temperature from degrees Fahrenheit (F˚) to degrees Celsius (C˚) is C˚=59F˚−1609. 1) Write a formula to convert from degrees Celsius to degrees Fahrenheit by solving for F˚ in the equation above. 2) Are the equations from the problem statement and from part 1 inverses? EXPLAIN

Answer 1

Explanation:

Given the formula to convert a temperature from degrees Fahrenheit (F˚) to degrees Celsius (C˚) as C˚=5/9F˚−1609.

To write the formula to convert °C to °F , we will make °F the subject of the formula

Add 1609 to both sides of the equation

C˚+1609=5/9F˚−1609.+1609

C+1609 = 5/9F

Cross multiply

9(C+1609) = 5F

Divide both sides by 5

9/5 (C+1609) = F

Hence the formula to convert from degrees Celsius to degrees Fahrenheit is 9/5 (C+1609) = F.

B) To check whether they are inverses we need to check if F(C) = C(F)

To get F(C) we will substitute F into C as shown;

F = 9/5 (C+1609)

C˚=5/9F˚−1609.

F(C) = 9/5 ((5/9F˚−1609.)+1609)

F(C) = 9/5 * 5F/9 -1609 + 1609

F(C) = 9/5 * 5F/9

F(C) = 45F/45

F(C) = F

Similarly for C(F)

C(F) = (5/9(9/5 (C+1609))˚−1609.

C(F) = (C+1609) - 1609

C(F) = C

This shows that both equations are inverses of each other