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Answer :
We start with the Celsius-to-Fahrenheit conversion formula given by
[tex]$$
F=\frac{9}{5}C+32.
$$[/tex]
Step 1. Finding the inverse formula (Fahrenheit to Celsius):
1. Write the given equation:
[tex]$$
F=\frac{9}{5}C+32.
$$[/tex]
2. Subtract 32 from both sides:
[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]$$
C=(F-32)\frac{5}{9}.
$$[/tex]
This inverse formula shows that for each Fahrenheit temperature [tex]$F$[/tex], there is exactly one corresponding Celsius temperature [tex]$C$[/tex], so the inverse is indeed a function.
Step 2. Using the inverse to find the Celsius temperature corresponding to [tex]$35^\circ F$[/tex]:
Substitute [tex]$F=35$[/tex] into the inverse formula:
[tex]$$
C=(35-32)\frac{5}{9}.
$$[/tex]
1. Compute the subtraction inside the parentheses:
[tex]$$
35 - 32 = 3.
$$[/tex]
2. Multiply by [tex]$\frac{5}{9}$[/tex]:
[tex]$$
C = 3 \times \frac{5}{9}.
$$[/tex]
3. This simplifies to:
[tex]$$
C = \frac{15}{9} \approx 1.6666666666666667.
$$[/tex]
Thus, the Celsius temperature corresponding to [tex]$35^\circ F$[/tex] is approximately [tex]$1.67^\circ C$[/tex].
Final Answers:
a. The inverse of the given formula is
[tex]$$
C=(F-32)\frac{5}{9},
$$[/tex]
and it is a function.
b. The Celsius temperature corresponding to [tex]$35^\circ F$[/tex] is approximately [tex]$1.67^\circ C$[/tex].
[tex]$$
F=\frac{9}{5}C+32.
$$[/tex]
Step 1. Finding the inverse formula (Fahrenheit to Celsius):
1. Write the given equation:
[tex]$$
F=\frac{9}{5}C+32.
$$[/tex]
2. Subtract 32 from both sides:
[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]$$
C=(F-32)\frac{5}{9}.
$$[/tex]
This inverse formula shows that for each Fahrenheit temperature [tex]$F$[/tex], there is exactly one corresponding Celsius temperature [tex]$C$[/tex], so the inverse is indeed a function.
Step 2. Using the inverse to find the Celsius temperature corresponding to [tex]$35^\circ F$[/tex]:
Substitute [tex]$F=35$[/tex] into the inverse formula:
[tex]$$
C=(35-32)\frac{5}{9}.
$$[/tex]
1. Compute the subtraction inside the parentheses:
[tex]$$
35 - 32 = 3.
$$[/tex]
2. Multiply by [tex]$\frac{5}{9}$[/tex]:
[tex]$$
C = 3 \times \frac{5}{9}.
$$[/tex]
3. This simplifies to:
[tex]$$
C = \frac{15}{9} \approx 1.6666666666666667.
$$[/tex]
Thus, the Celsius temperature corresponding to [tex]$35^\circ F$[/tex] is approximately [tex]$1.67^\circ C$[/tex].
Final Answers:
a. The inverse of the given formula is
[tex]$$
C=(F-32)\frac{5}{9},
$$[/tex]
and it is a function.
b. The Celsius temperature corresponding to [tex]$35^\circ F$[/tex] is approximately [tex]$1.67^\circ C$[/tex].
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