How to find domain and range of a rational equation using inverse

The video tutorial covers the concepts of domain and inverse functions, explaining how to find the domain by identifying values that make the denominator zero. It then moves on to finding the inverse of a function by swapping variables and solving for the new variable. The tutorial also discusses solving equations with variables in the denominator, simplifying expressions using the distributive property, and factoring to solve equations. The session concludes with a graphical representation of the functions discussed.

What is the domain of a function?

• All negative numbers

• All positive numbers

• All numbers except those that make the denominator zero

• All real numbers

Why do we swap variables when finding the inverse of a function?

• To make the equation easier to solve

• Because the graph of the inverse swaps the x and y axes

• To eliminate fractions

• To simplify the domain

What is the first step in solving an equation with a variable in the denominator?

• Add the variable to both sides

• Subtract the variable from both sides

• Multiply both sides by the variable

• Divide both sides by the variable

How can you simplify an equation using the distributive property?

• By adding like terms

• By dividing each term by the same number

• By subtracting terms from both sides

• By multiplying each term inside the parentheses by the term outside

What is the purpose of factoring in solving equations?

• To simplify the equation

• To isolate the variable

• To combine like terms

• To find the greatest common factor

What is the domain of the inverse function f inverse of x = (-4x - 1) / (x - 2)?

• All positive numbers

• All numbers except x cannot equal 2

• All numbers except x cannot equal -4

• All real numbers

What happens when a quantity is divided by itself?

• It equals infinity

• It equals the original quantity

• It equals one

• It equals zero