Answer :
(a) To express the temperature in degrees Celsius C as a function of the temperature in degrees Fahrenheit F, we need to rearrange the equation F(C) = (9/5)C + 32 to solve for C.
F(C) = (9/5)C + 32
Subtract 32 from both sides:
F(C) - 32 = (9/5)C
Multiply both sides by (5/9):
(5/9)(F(C) - 32) = C
So, the function to convert temperature from Fahrenheit to Celsius is:
C(F) = (5/9)(F - 32)
(b) To verify that C = C(F) is the inverse of F = F(C), we substitute C(F) into F(C) and F(C(F)) into C(F) and check if we get the original values:
F(C(F)) = F[(5/9)(F - 32)]
= (9/5)[(5/9)(F - 32)] + 32
= F - 32 + 32
= F
C(F(C)) = C[(9/5)C + 32]
= (5/9)[(9/5)C + 32 - 32]
= C
Since both C(F(C)) and F(C(F)) result in the original values C and F, we can conclude that C = C(F) is the inverse of F = F(C).
(c) If it is 70 degrees Fahrenheit, we can use the function C(F) = (5/9)(F - 32) to find the temperature in degrees Celsius:
C(70) = (5/9)(70 - 32)
= (5/9)(38)
≈ 21.11 degrees Celsius
Therefore, if it is 70 degrees Fahrenheit, the temperature in degrees Celsius would be approximately 21.11 degrees Celsius.
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