Find the inverse of a linear function

The video tutorial explains how to find the inverse of a function by swapping X and Y coordinates, both graphically and algebraically. It provides a step-by-step guide to solving for Y, introduces inverse notation, and discusses different representations of the inverse. The tutorial also covers the domain and range of inverse functions, emphasizing that for linear functions, both are all real numbers.

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

• Add a constant to both sides

• Divide by a constant

• Multiply by a constant

• Swap the X and Y coordinates

When solving for Y in the inverse function, what should you do after eliminating the denominator?

• Add the constant to both sides

• Subtract the constant from both sides

• Swap X and Y again

• Multiply by the coefficient of Y

Which of the following is a correct representation of the inverse function Y inverse = (2X + 1) / 3?

• Y inverse = X/2 + 1/3

• Y inverse = 2/3X + 1/3

• Y inverse = 2X - 1/3

• Y inverse = 3X + 2

What is the domain of the inverse of a linear function?

• Negative integers

• All real numbers

• Positive integers

• Complex numbers

Why is it unnecessary to find the domain of the inverse to determine the range for linear functions?

• Because the domain is always limited

• Because the range is always negative

• Because the domain and range are both all real numbers

• Because the range is always positive