Answer:
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