Learning Objectives:

__Math Tutoring on Determining Inverse Functions__

If a function is defined so that each range element or** ****y** value is used only once then it is a **One-to-one Function**. If every **y** value is only paired with one **x** value we have a special type of function called a **One-to-one Function** and in math tutoring a **Horizontal** **Line Test** helps to determine graphically whether a function is one-to-one. If a horizontal line does not intersect the graph of a function in more than one point it is a **One-to-one Function** and what is so important about this is that only **One-to-one Function** have **Inverse Functions**. If **f** is a function from a set **A** to a set **B**, then an Inverse Function of **‘f’** is a function from** ****B** to **A** , with the property that a round trip or composition from **A** to **B** to** ****A'** ( or from **B**** **to** ****A **to** ****B** ) returns each element of the initial set to itself. Thus if an input** ****x** into the function **f** produces an output **y**, then in putting **y** into the inverse function produces the output **x** and vice versa.

** f (g(x)) = g(f(x)) = x**

Lastly, a function that has an inverse is called **Invertible**; the **Inverse Function** is then uniquely determined by** ****f**** **and it's denoted by **f ^{ -1}**.

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**Hook Questions:**

*1. **What is a one to one function? *

*2. ** How does one to one function be related to Inverse function?*

*3. ** What is meant by invertible?*

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