Find inverse of a rational equation with two variables in numerator and denominator

The video tutorial explains how to find the inverse of a function, focusing on the function y = (3X - 5) / (2X + 1). It covers the concepts of domain and range, emphasizing the importance of setting the denominator equal to zero to find the domain. The tutorial provides a step-by-step guide to finding the inverse, including swapping variables and solving equations with variables on both sides. It concludes with a discussion on the domain and range of the inverse function, reinforcing previously learned concepts.

What is the domain of the function y = (3X - 5) / (2X + 1)?

• All real numbers except X = 1/2

• All real numbers

• All real numbers except X = -1/2

• All real numbers except X = 0

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

• Swap X and Y

• Multiply both sides by the denominator

• Add the same value to both sides

• Factor out the variable

Why is it important to remove a variable from the denominator when finding an inverse?

• To ensure the variable is isolated

• To simplify the equation

• To make the equation linear

• To avoid division by zero

How do you solve for Y after factoring it out in the inverse function?

• Add the same value to both sides

• Multiply both sides by the denominator

• Divide by the remaining expression

• Subtract the same value from both sides

What is the relationship between the domain of the original function and the range of its inverse?

• They are the same

• The range of the original is the domain of the inverse

• The domain of the original is the range of the inverse

• They are unrelated