High School

The formula [tex]y=f(x)=\frac{9}{5}x+32[/tex] is used to convert from [tex]x[/tex] degrees Celsius to [tex]y[/tex] degrees Fahrenheit. The formula [tex]y=g(x)=\frac{5}{9}(x-32)[/tex] is used to _______.

a) convert from [tex]y[/tex] degrees Fahrenheit to [tex]x[/tex] degrees Celsius
b) convert from [tex]x[/tex] degrees Fahrenheit to [tex]y[/tex] degrees Celsius
c) convert from [tex]y[/tex] degrees Celsius to [tex]x[/tex] degrees Fahrenheit
d) convert from [tex]x[/tex] degrees Celsius to [tex]y[/tex] degrees Fahrenheit

Answer :

The formula (y=g(x)=5/9(x-32)) is used to convert from (x) degrees Fahrenheit to (y) degrees Celsius, which corresponds to option B.

The given formula \( g(x) = \frac{5}{9}(x - 32) \) is designed to convert temperatures from Fahrenheit to Celsius. It involves subtracting 32 from the temperature in Fahrenheit to get the difference in degrees, then multiplying by \( \frac{5}{9} \) to convert this difference to Celsius. Therefore, option B is correct as it accurately describes the conversion from Fahrenheit to Celsius. Conversely, the formula \( f(x) = \frac{9}{5}x + 32 \) is used to convert temperatures from Celsius to Fahrenheit, making option B the appropriate choice.

Correct option: Option B