# 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.**