To convert temperatures from degrees Celsius to degrees Fahrenheit, you can use the function upper F left-parenthesis x right-parenthesis equals Start Fraction 9 over 5 End Fraction x plus 32 where x is the temperature in degrees Celsius. To convert temperatures from degrees Kelvin to degrees Celsius, you can use the function upper C left-parenthesis x right-parenthesis equals x minus 273.15, where x is the temperature in degrees Kelvin. Find the composite function that can be used to convert temperatures from degrees Kelvin to degrees Fahrenheit.

Question

(1 point)
Responses

left-parenthesis upper C circle upper F right-parenthesis left-parenthesis x right-parenthesis equals Start Fraction 9 over 5 End Fraction x minus 241.15
Image with alt text: left-parenthesis upper C circle upper F right-parenthesis left-parenthesis x right-parenthesis equals Start Fraction 9 over 5 End Fraction x minus 241.15

left-parenthesis upper F circle upper C right-parenthesis left-parenthesis x right-parenthesis equals Start Fraction 9 over 5 End Fraction x minus 241.15
Image with alt text: left-parenthesis upper F circle upper C right-parenthesis left-parenthesis x right-parenthesis equals Start Fraction 9 over 5 End Fraction x minus 241.15

left-parenthesis upper C circle upper F right-parenthesis left-parenthesis x right-parenthesis equals Start Fraction 9 over 5 End Fraction left-parenthesis x minus 273.15 right-parenthesis plus 32
Image with alt text: left-parenthesis upper C circle upper F right-parenthesis left-parenthesis x right-parenthesis equals Start Fraction 9 over 5 End Fraction left-parenthesis x minus 273.15 right-parenthesis plus 32

left-parenthesis upper F circle upper C right-parenthesis left-parenthesis x right-parenthesis equals Start Fraction 9 over 5 End Fraction left-parenthesis x minus 273.15 right-parenthesis plus 32

Answer 1

To find the composite function that converts temperatures from degrees Kelvin to degrees Fahrenheit, we start with the two functions given:

1. From Kelvin to Celsius: \[ C(x) = x - 273.15 \]

2. From Celsius to Fahrenheit: \[ F(x) = \frac{9}{5}x + 32 \]

To create the composite function \( F(C(x)) \), which converts Kelvin to Fahrenheit, we substitute \( C(x) \) into \( F(x) \):

1. Substitute \( C(x) = x - 273.15 \) into \( F(x) \): \[ F(C(x)) = F(x - 273.15) = \frac{9}{5}(x - 273.15) + 32 \]

2. Now simplify the expression: \[ F(C(x)) = \frac{9}{5}(x - 273.15) + 32 \] \[ = \frac{9}{5}x - \frac{9}{5} \cdot 273.15 + 32 \] \[ = \frac{9}{5}x - 490.07 + 32 \] \[ = \frac{9}{5}x - 458.07 \]

Now, looking at the response options, we need the version that expresses this whole process correctly, which is: \[ \left( C \circ F \right)(x) = \frac{9}{5}(x - 273.15) + 32 \]

Thus, the correct composite function that converts Kelvin to Fahrenheit is: \[ \left( F \circ C \right)(x) = \frac{9}{5}(x - 273.15) + 32 \]

Matching it with the provided options, the correct one would be: \[ \boxed{\left( C \circ F \right)(x) = \frac{9}{5}(x - 273.15) + 32} \]