Answer :
To find the formula for converting temperature from degrees Fahrenheit to degrees Celsius, we need to start with the original formula that converts Celsius to Fahrenheit:
[tex]\[ F(C) = \frac{9}{5}C + 32 \][/tex]
To find the inverse function, we need to solve this equation for [tex]\(C\)[/tex] in terms of [tex]\(F\)[/tex]. Here's how you do that step by step:
1. Start with the given formula:
[tex]\[ F = \frac{9}{5}C + 32 \][/tex]
2. Subtract 32 from both sides to isolate the term with [tex]\(C\)[/tex] on one side:
[tex]\[ F - 32 = \frac{9}{5}C \][/tex]
3. Multiply both sides by [tex]\(\frac{5}{9}\)[/tex] to solve for [tex]\(C\)[/tex]:
[tex]\[ C = \frac{5}{9}(F - 32) \][/tex]
This is the formula you use to convert a temperature from degrees Fahrenheit to degrees Celsius.
So, the answer is:
[tex]\[ C(F) = \frac{5}{9}F - \frac{5}{9} \times 32 \][/tex]
By completing the calculations, we can break it down as:
1. The conversion factor is [tex]\(\frac{5}{9}\)[/tex], approximately [tex]\(0.5556\)[/tex].
2. The value to subtract due to multiplying [tex]\(32\)[/tex] by [tex]\(\frac{5}{9}\)[/tex] is approximately [tex]\(17.778\)[/tex].
Therefore, the conversion formula is:
[tex]\[ C(F) = 0.5556F - 17.778 \][/tex]
[tex]\[ F(C) = \frac{9}{5}C + 32 \][/tex]
To find the inverse function, we need to solve this equation for [tex]\(C\)[/tex] in terms of [tex]\(F\)[/tex]. Here's how you do that step by step:
1. Start with the given formula:
[tex]\[ F = \frac{9}{5}C + 32 \][/tex]
2. Subtract 32 from both sides to isolate the term with [tex]\(C\)[/tex] on one side:
[tex]\[ F - 32 = \frac{9}{5}C \][/tex]
3. Multiply both sides by [tex]\(\frac{5}{9}\)[/tex] to solve for [tex]\(C\)[/tex]:
[tex]\[ C = \frac{5}{9}(F - 32) \][/tex]
This is the formula you use to convert a temperature from degrees Fahrenheit to degrees Celsius.
So, the answer is:
[tex]\[ C(F) = \frac{5}{9}F - \frac{5}{9} \times 32 \][/tex]
By completing the calculations, we can break it down as:
1. The conversion factor is [tex]\(\frac{5}{9}\)[/tex], approximately [tex]\(0.5556\)[/tex].
2. The value to subtract due to multiplying [tex]\(32\)[/tex] by [tex]\(\frac{5}{9}\)[/tex] is approximately [tex]\(17.778\)[/tex].
Therefore, the conversion formula is:
[tex]\[ C(F) = 0.5556F - 17.778 \][/tex]