The function f(x)=1.8x+32

Question

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:

$$(f\circ g)(k)=1.8k-463.4$$