Find the Inverse Function Algebraically

The video tutorial explains how to find the inverse of a function algebraically, addressing common student challenges. It outlines the steps to replace function notation, swap variables, and solve for the inverse. The tutorial also covers graphical interpretations, using Desmos for verification, and provides detailed examples, including cubic and radical functions. The importance of understanding domain and range swaps in inverse functions is emphasized.

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

• Check the domain

• Replace F of X with Y

• Solve for X

• Graph the function

When solving for the inverse of a linear function, what is the typical domain?

• All real numbers

• Positive integers

• Rational numbers

• Negative integers

In the context of inverse functions, what does swapping X and Y help to achieve?

• Solving for the original function

• Determining the function's slope

• Identifying the function's symmetry

• Finding the range

What is a key consideration when dealing with inverse functions that have fractions?

• Avoiding division by zero

• Minimizing the domain

• Ensuring the numerator is zero

• Maximizing the range

How do you determine the range of an inverse function?

• By solving for Y

• By graphing the inverse function

• By finding the domain of the original function

• By checking the symmetry

What is the domain of a cubic function's inverse?

• Negative numbers only

• Positive numbers only

• Rational numbers

• All real numbers

Why are cubic functions unrestricted in their domain and range?

• Because they are quadratic

• Because they can take any real number

• Because they are symmetrical

• Because they are linear

What is a common restriction when dealing with inverse functions that include radicals?

• The variable cannot be negative

• The variable must be positive

• The variable must be an integer

• The variable cannot be zero

How do you handle a variable in the denominator when finding an inverse function?

• Multiply both sides by the denominator

• Divide both sides by the denominator

• Add the denominator to both sides

• Subtract the denominator from both sides

What is the range of an inverse function with a cube root in the denominator?

• Only negative numbers

• All real numbers except zero

• Only positive numbers

• All integers