Inverse Functions and Their Properties

The video tutorial explains how to find the inverse of a function. It begins with swapping the X and Y variables, then solving for Y using properties of equality. The tutorial covers using reciprocals to undo multiplication and graphing both the original and inverse functions. Finally, it demonstrates reflecting functions over the XY line to verify the inverse.

What is the first step in finding the inverse of a function that is already in y-form?

• Solve for x

• Graph the function

• Use the reciprocal

• Swap the x and y coordinates

When finding the inverse of a function, what do you swap?

• The coefficients

• The numerator and denominator

• The slope and intercept

• The x and y coordinates

What property is used to isolate the y variable when solving for y?

• Addition property of equality

• Multiplication property of equality

• Subtraction property of equality

• Division property of equality

What is the first step in solving for y in the inverse function?

• Divide by 2/3

• Multiply by 2/3

• Subtract 2 from both sides

• Add 2 to both sides

How do you undo multiplication by a fraction?

• Multiply by the reciprocal

• Subtract the fraction

• Divide by the reciprocal

• Add the fraction

Why is it important to use parentheses when multiplying by the reciprocal?

• To avoid division errors

• To simplify the equation

• To make the equation look neat

• To ensure the correct order of operations

What is the result of multiplying a number by its reciprocal?

• Negative one

• The number itself

• One

• Zero

What is the y-intercept of the original function in the example?

• 2

• -3

• 0

• 3

What is the slope of the inverse function in the example?

• 1/3

• 3

• -3

• 2/3

How are the original function and its inverse related on a graph?

• They are reflections over the line y=x

• They have the same slope

• They are parallel

• They intersect at the origin