Given two functions that are inverses find the derivative

The video tutorial explains the concept of inverse functions, highlighting that the domain and range are swapped and reflected about the Y=X line. It demonstrates how to apply this understanding to solve a problem involving reciprocal slopes, using given values to calculate the result. The tutorial emphasizes the importance of knowing the relationship between inverse functions and their slopes.

What is the basic property of inverse functions regarding their domain and range?

• They are identical.

• They are swapped.

• They are doubled.

• They are halved.

How are the slopes of inverse functions related at swapped points?

• They are squared.

• They are negative.

• They are reciprocals.

• They are equal.

If M'(5) is given, how can you find N'(9) for inverse functions M and N?

• Take the reciprocal of M'(5).

• Add 5 to M'(5).

• Multiply M'(5) by 2.

• Subtract 5 from M'(5).

What is the result of reciprocating the slope -8/111?

• -111/8

• 111/8

• 8/111

• -8/111

Why is it important to understand the relationship between inverse functions and their slopes?

• To find the area under the curve.

• To calculate derivatives accurately.

• To solve quadratic equations.

• To understand their graphical representation.