Question
The formula C = (5/9) (F −32), where F ≥ −459.67 expresses the temperature “C” in degrees Celsius as a function of the temperature on the \F" scale, in Fahrenheit. Find a formula for the function inverse and interpret it. What is the domain of this inverse function?
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Answer to a math question The formula C = (5/9) (F −32), where F ≥ −459.67 expresses the temperature “C” in degrees Celsius as a function of the temperature on the \F" scale, in Fahrenheit. Find a formula for the function inverse and interpret it. What is the domain of this inverse function?
Eliseo
4.6102 Answers
1. Start with the given formula:
C = \frac{5}{9} (F - 32)
2. Multiply both sides by 9 to clear the fraction:
9C = 5(F - 32)
3. Divide both sides by 5 to isolateF - 32
\frac{9C}{5} = F - 32
4. Add 32 to both sides to solve forF
F = \frac{9C}{5} + 32
So, the inverse function is:
F = \frac{9C}{5} + 32
The domain of this inverse function, corresponding to the range of the original function, is:
C \geq \frac{5}{9}(-459.67 - 32)
Calculating this,
C \geq \frac{5}{9}(-491.67) \approx -273.15
Therefore, the domain of the inverse function is:
C \geq -273.15
2. Multiply both sides by 9 to clear the fraction:
3. Divide both sides by 5 to isolate
4. Add 32 to both sides to solve for
So, the inverse function is:
The domain of this inverse function, corresponding to the range of the original function, is:
Calculating this,
Therefore, the domain of the inverse function is:
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