# How do you verify an inverse function?

**inverse of**a

**function**, you should

**verify**on your own that the

**inverse**you obtained was correct, time permitting. Show that f(g(x)) = x. Show that g(f(x)) = x.

Likewise, how can you tell if two functions are inverses?

Remember, if the **two** graphs are symmetric with respect to the line y = x (mirror images over y = x ), then they are **inverse functions**. But, we need a way to check without the graphs, because we won't always know what the graphs look like! then f(x) and g(x) are **inverse functions**.

Additionally, how do you find the inverse of a function from a graph? So if you're asked to **graph** a **function** and its **inverse**, all you have to do is **graph** the **function** and then switch all x and y values in each point to **graph** the **inverse**. Just look at all those values switching places from the f(x) **function** to its **inverse** g(x) (and back again), reflected over the line y = x.

Correspondingly, where is inverse on a calculator?

**How to Draw the Inverse of a Function on the TI-84 Plus**

- Enter your functions in the Y= editor.
- Press [2nd][MODE] to access the Home screen.
- Press [2nd][PRGM][8] to insert the DrawInv function.
- Press [ALPHA][TRACE] and choose the name of the function you entered.
- Press [ENTER] to display the graph of your function and draw the inverse of your function.

How do you find the composition of a function?

**Summary**

- "Function Composition" is applying one function to the results of another.
- (g º f)(x) = g(f(x)), first apply f(), then apply g()
- We must also respect the domain of the first function.
- Some functions can be de-composed into two (or more) simpler functions.