C(F) = 5/9F-17.778. (b) Re-write equation C(F) as F(C) and verify that F(C) = C1(F) ie it is an inverse function.

Answer 1

C = (5/9)F - 17.778 = (5/9) (F - 32) <--- this is the EXACT FORMULA

(9/5)C = F - 32

(9/5)C + 32 = F

check: Let t be the temperature

F(C(t)) =

(5/9) [ (9/5)t + 32 -32] =

(5/9) [ (9/5)t ] = t

AND

C(F(t)) =

(9/5) [ (5/9)(t - 32)] + 32 =

(9/5)(5//9)(t-32) + 32 =

t - 32 + 32 = t