Finding Inputs from Outputs in Functions

In this video tutorial, the instructor explains how to find the input of a function given its output. The function f(x) = 5x + 12 is used as an example. The video walks through setting up an equation with a given output value, solving for the input x, and verifying the solution by substituting back into the function. The process involves basic algebraic operations such as subtraction and division to isolate the variable x.

What is the main topic discussed in the video?

• Finding the output of a function given the input

• Finding the input of a function given the output

• Graphing linear functions

• Solving quadratic equations

What is the function presented in the video?

• f(x) = 2x + 5

• f(x) = 5x + 12

• f(x) = 4x + 9

• f(x) = 3x + 7

What is the given output value for the function?

• 30

• 27

• 20

• 15

What is the first step in setting up the equation to find the input?

• Add 12 to both sides

• Multiply both sides by 5

• Subtract 12 from both sides

• Divide both sides by 5

What equation is formed after setting up the problem?

• 5x = 27

• 5x = 15

• 5x = 12

• 5x = 20

What is the next step after forming the equation 5x = 15?

• Divide both sides by 5

• Multiply both sides by 5

• Subtract 5 from both sides

• Add 5 to both sides

What is the value of x after solving the equation?

• 5

• 4

• 3

• 2

How do you verify the solution for x?

• By checking with a calculator

• By graphing the function

• By substituting x back into the original function

• By solving a different equation

What is the result when x = 3 is substituted back into the function?

• 30

• 20

• 15

• 27

What operation is performed first when verifying the solution?

• Multiplication

• Division

• Subtraction

• Addition