Writing Inverse Equations
Find the inverse of the function, if it exists. If an inverse exists, show that \(f(f^{-1}(x))=x\) and \(f^{-1}(f(x))=x\) .
1. \(f(x)=3x-2\)
2. \(f(x)=2-2x\)
3. \(f(x)=x^3\)
4. \(f(x)=x^2-2\)
5. \(f(x)=x^2-2\) , \(x\geq 0\) . How is this different from #5 ?
Function Inverses in Context
6. Use the table below to create the function that converts Celsius to Fahrenheit. Then find the inverse function (converting to Celsius).
| \(C\) | 0 | 10 | 20 | 40 |
| \(F\) | 32 | 50 | 68 | 104 |
7. Write the function and its inverse that will convert Dollars to Euros and then Euros to Dollars if $1 will buy 0.92086 Euros.
For additional practice, go to Illustrative Mathematics and complete the tasks “Invertible or Not?”.
Also try the task: Temperature.
Check your solutions here.
