Answer :
To convert 68°F to Celsius: C(68) = 20°C. To convert 35°C to Fahrenheit: F(35) = 95°F. Verifying the inverse nature of the formulas, we showed that converting 20°C to Fahrenheit and back to Celsius returns the original 20°C, proving they are inverses.
To convert 68°F to Celsius using the given formula C(x) = 5/9(x – 32), we substitute x with 68:
C(68) = 5/9(68 – 32) = 5/9(36) = 20°C
To convert 35°C to Fahrenheit, we use the inverse of the Celsius to Fahrenheit formula, which is F(x) = (9/5)x + 32. So:
F(35) = (9/5)×35 + 32 = 63 + 32 = 95°F
To verify that the equations are inverses of one another, we will show that applying them sequentially returns the original value:
Let's start with a Celsius temperature, say 20°C:
F(20) = (9/5)×20 + 32 = 36 + 32 = 68°F
Now converting back to Celsius:
C(68) = 5/9(68 – 32) = 5/9(36) = 20°C
Since we get back our original Celsius value, this confirms that the two formulas are indeed inverses of each other.
