Inverse Functions and Their Properties

The video tutorial explains how to find the inverse of a given function. It starts by introducing the concept of inverse functions, which undo the operations of the original function. The tutorial then provides a step-by-step guide on how to write the original function in terms of x and y, interchange the variables, and solve for y to find the inverse function. The process involves cross-multiplying and factoring to isolate y, and finally, replacing y with inverse function notation. The tutorial concludes with the final expression of the inverse function.

What is the purpose of an inverse function?

• To double the output of the original function

• To reverse the operation of the original function

• To square the input of the original function

• To halve the input of the original function

What is the first step in finding the inverse of a function?

• Multiply the function by 2

• Interchange the x and y variables

• Subtract 3 from the function

• Add 5 to the function

When interchanging variables, what does the output of the original function become?

• The new coefficient

• The new input

• The new constant

• The new output

What is the equation form after interchanging x and y?

• x = (5x + 2) / (x - 3)

• y = (5y + 2) / (y - 3)

• x = (5y + 2) / (y - 3)

• y = (5x + 2) / (x - 3)

What operation can be used to eliminate the fraction in the equation?

• Addition

• Subtraction

• Cross multiplication

• Division

What is the next step after distributing in the equation?

• Subtract 5y from both sides

• Multiply by 3

• Add 5 to both sides

• Divide by x

What is the purpose of factoring out y in the equation?

• To add a constant

• To simplify the equation

• To eliminate x

• To isolate y on one side

What is the final form of the inverse function?

• f(x) = (3x + 2) / (x - 5)

• f(x) = (2x + 3) / (5x - 3)

• f(x) = (5x + 2) / (x - 3)

• f(x) = (x + 2) / (3x - 5)

What is the notation used for the inverse function?

• f double prime of x

• f inverse of x

• f prime of x

• f(x)

What is the final step in expressing the inverse function?

• Add 5 to the equation

• Subtract 2 from the equation

• Replace y with f inverse of x

• Replace x with y