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# HL AI – Inverse Functions

##### One to One Functions

The mapping diagram below shows that each number in the domain maps to a unique number in the range.

Put a number in the range into the inverse function and it will send you back to the domain number of the function.

Each x number has a unique y number.

The mapping diagram below shows that each number in the domain maps to a unique number in the range.

Put a number in the range into the inverse function and it will send you back to the domain number of the function.

Each x number has a unique y number.

##### Many to One Functions

The mapping diagram below shows that more than one number in the domain map to the same number in the range.

These types of function have no inverse.

Two x numbers give us the same y number.

##### Relationships, Functions, Functions with inverses

Try putting a vertical line on the graph. Does it go through the graph twice? Yes, It is a not function.

Try putting a vertical line on the graph. Does it go through the graph twice? No, It is a function.

Try putting a horizontal line on the graph. Does it go through the graph twice? Yes, it is a function without an inverse.

Try putting a vertical line on the graph. Does it go through the graph twice? No, it is a function.

Try putting a horizontal line on the graph. Does it go through the graph twice? No, it is a function with an inverse.

##### Functions, domains, inverses, range

The range of a function is the domain of the inverse function.

The range of the inverse function is the domain of the function.