Inverse of a function with x in numerator and denominator

The video tutorial explains how to solve an equation by replacing F of X with Y, swapping X and Y, and solving for Y. It highlights common student difficulties, such as dealing with variables on both sides of the equation, and demonstrates factoring to simplify the problem. The tutorial also covers understanding the domain and range of functions and their inverses, emphasizing that the domain of the inverse is the range of the original function.

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

• Replace F(x) with Y

• Swap X and Y

• Solve for X

• Graph the function

When solving an equation with variables on both sides, what should you do?

• Divide them

• Add them together

• Multiply them

• Get them to the same side

How can you solve for Y when you have Y on both sides of the equation?

• Use a graphing calculator

• Combine like terms

• Factor out Y

• Add a constant

What is the domain of the inverse function if the original function's domain is all real numbers except 0?

• All real numbers

• All real numbers except 2

• Negative infinity to 0

• 0 to infinity

Why is it useful to find the inverse of a function when determining the range?

• It simplifies the function

• It provides the domain of the inverse, which is the range of the original function

• It eliminates the need for a calculator

• It changes the function's graph