Finding Inverses of Functions: A Step-by-Step Guide

This video tutorial explains how to find the inverse of various types of functions, including linear, cubic, square root, cube root, and rational functions. The instructor provides step-by-step instructions for each example, demonstrating how to switch variables, isolate the desired variable, and solve for the inverse function. The video also highlights different methods for simplifying the final expression and offers tips for handling more complex functions.

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

• Switch x with y

• Isolate the y variable

• Replace f(x) with y

• Divide both sides by the coefficient of y

How do you solve for y in the equation x = y^3 + 8?

• Add 8 to both sides

• Divide both sides by 3

• Take the cube root of both sides

• Subtract 8 from both sides

What is the inverse function of f(x) = x^3 + 8?

• y = x^3 + 8

• y = 3√(x - 8)

• y = x/3 + 8/3

• y = (x - 8)^3

In the equation x = √(y + 2) - 5, what is the next step after adding 5 to both sides?

• Take the square root of both sides

• Divide both sides by 2

• Subtract 2 from both sides

• Square both sides

What is the final form of the inverse function for f(x) = √(x + 2) - 5?

• y = x + 5 - √2

• y = √(x + 7)

• y = x^2 + 10x + 23

• y = (x + 5)^2 - 2

How do you remove the cube root symbol in the equation x = ³√(y + 4) - 2?

• Subtract 2 from both sides

• Cube both sides

• Add 4 to both sides

• Divide both sides by 3

What is the inverse function of f(x) = ³√(x + 4) - 2?

• y = ³√(x - 2) + 4

• y = (x + 2)^3 + 4

• y = (x + 2)^3 - 4

• y = x^3 + 4

In the complex function f(x) = (3x - 7)/(4x + 3), what is the first step to find its inverse?

• Switch x with y

• Cross multiply

• Isolate the y variable

• Write x as x/1 and cross multiply

After isolating terms with y on one side in the complex function, what should you do next?

• Divide both sides by x

• Factor out y

• Add 7 to both sides

• Subtract 3x from both sides

What is the inverse function of f(x) = (3x - 7)/(4x + 3)?

• y = (3x + 7)/(3 - 4x)

• y = (3x + 7)/(3 - 4x)

• y = (3x - 7)/(4x - 3)

• y = (3x + 7)/(4x + 3)