## Related questions with answers

When traveling outside of the United States it is often useful to be able to convert between temperatures measured using the Fahrenheit scale and temperatures measured using the Celsius scale. The standard formula for determining temperature in degrees Fahrenheit when given the temperature in degrees Celsius is, $F=\frac{9}{5} C+32$. We can write this formula using function notation by letting $F = g(C)$ and writing $g(C)=\frac{9}{3} C+32$. The function g defines a process for converting degrees Celsius to degrees Fahrenheit. a. State the meaning of g(100) and evaluate g(100). b. Solve the equation $g(C)=212$ and explain how you arrived at your answer. c. Define a function h that converts Fahrenheit temperature to its Celsius temperature. (Hint. Generalize the steps you described in part (b) that reverses of g. You can also solve $F=\frac{9}{3} C+32$ for C.) d. Determine the values of g(100) and h(212). e. Determine the values of g(h(212)) and h(g(100)) without performing any calculations. What do you notice about the relationship between g and h? f. Represent the value of g(h(n)). Represent the value of h(g(k)). What do you notice about the relationship between g and h?

Solution

Verified**a)** The meaning of the $g(100)$ is that it represents the temperature in Fahrenheit if we are given a temperature of $100$ degrees Celsius.

Let's evaluate $g(100)$:

$\begin{aligned} g(C)&=\frac{9}{5}C+32\\ g(100)&\overset{(1)}=\frac{9}{5}\cdot100+32\\ g(100)&=\frac{900}{5}+32\\ g(100)&=180+32\\ g(100)&\overset{(2)}=212\\ \end{aligned}$

The result $212$ represents temperature in Fahrenheit.

$(1)$ - Substitute $C$ with $100$ $(2)$ - The final result

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