Question

The function f(x)=1.8x+32
is used to convert from degrees Celsius to degrees Fahrenheit, where x is a temperature in degrees Celsius. The function g(k)=k−273
is used to convert from degrees Kelvin to degrees Celsius, where k is a temperature in degrees Kelvin. What function can be used to convert from degrees Kelvin to degrees Fahrenheit?

Enter the missing values.

(1 point)
(f∘g)(k)=
$$

Answer 1

To find the function that converts from degrees Kelvin to degrees Fahrenheit, we will first use the function \( g(k) \) to convert Kelvin to Celsius, and then use the function \( f(x) \) to convert Celsius to Fahrenheit.

Given:
- \( f(x) = 1.8x + 32 \) (converts Celsius to Fahrenheit)
- \( g(k) = k - 273 \) (converts Kelvin to Celsius)

Now, we find \( (f \circ g)(k) \), which means we will apply \( g(k) \) first and then apply \( f \) to the result.

1. Calculate \( g(k) \):
\[
g(k) = k - 273
\]

2. Substitute \( g(k) \) into \( f(x) \):
\[
(f \circ g)(k) = f(g(k)) = f(k - 273)
\]

3. Now, substitute \( k - 273 \) into \( f(x) \):
\[
f(k - 273) = 1.8(k - 273) + 32
\]

4. Distributing \( 1.8 \):
\[
= 1.8k - 1.8 \times 273 + 32
\]

5. Calculate \( 1.8 \times 273 \):
\[
1.8 \times 273 = 495.4
\]

6. So we have:
\[
= 1.8k - 495.4 + 32
\]

7. Combine the constants:
\[
= 1.8k - 495.4 + 32 = 1.8k - 463.4
\]

Thus, the function that converts from degrees Kelvin to degrees Fahrenheit is:

\[
(f \circ g)(k) = 1.8k - 463.4
\]

You can fill in the missing values with:

\[
(f \circ g)(k) = 1.8k - 463.4
\]