Answer:
[tex]f(x)=\dfrac{9}{5}x+32[/tex] converts Celsius to Fahrenheit.
[tex]g(x)=\dfrac{5(x-32)}{9}[/tex] converts Fahrenheit to Celsius.
Step-by-step explanation:
Write given data in the table
[tex]\begin{array}{cc}x&f(x)\\^{\circ}\text{C}&^{\circ}\text{F}\\20&68\\30&86\end{array}[/tex]
Let the expression for the function be
[tex]f(x)=ax+b[/tex]
Note, that this equation is linear equation and it is well-known fact that the Celsius to Fahrenheit dependence is linear.
Substitute corresponding values into this expression:
[tex]68=20a+b\\ \\86=30a+b[/tex]
Subtract these two equations:
[tex]86-68=30a-20a\\ \\10a=18\\ \\a=\dfrac{9}{5}[/tex]
Substitute it into the first equation:
[tex]68=20\cdot \dfrac{9}{5}+b\Rightarrow b=68-36=32[/tex]
So,
[tex]f(x)=\dfrac{9}{5}x+32[/tex]
This is the function which converts Celsius to Fahrenheit.
And function
[tex]g(x)=\dfrac{5(x-32)}{9}[/tex] converts Fahrenheit to Celsius.
