Finding Inverses of Functions

The video tutorial explains how to find the inverse of a function using a step-by-step process. It begins with writing the function as a linear equation, swapping the X and Y variables, solving for Y, and finally writing the result in inverse notation. The tutorial also touches on graphing and simplifying the inverse function.

What is the initial function given in the problem?

• f(x) = 2x + 3

• f(x) = 3x - 4

• f(x) = x^2 + 1

• f(x) = 5x - 2

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

• Graph the function

• Write as a linear equation

• Solve for y

• Swap x and y

Why do we use x and y instead of f(x) when writing the function as a linear equation?

• To make it easier to solve for x

• To avoid confusion with output values

• To simplify the equation

• To make it easier to graph

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

• Graph the function

• Swap x and y

• Solve for y

• Simplify the equation

After swapping x and y, what is the next step?

• Simplify the equation

• Solve for y

• Write in inverse notation

• Graph the function

What operation is performed after adding 4 to both sides of the equation?

• Multiply by 3

• Divide by 3

• Add 3

• Subtract 4

What is the simplified form of the equation after solving for y?

• y = 1/3x + 4/3

• y = 3x + 4

• y = x/3 + 4/3

• y = x + 4

Why might it be difficult to graph the inverse function in its simplified form?

• It is not in slope-intercept form

• It lacks a clear y-intercept

• It has a complex slope

• It is not a linear equation

What is the result of dividing the terms by 3 in the equation x + 4 = 3y?

• y = 1/3x + 4/3

• y = x + 4/3

• y = 3x + 4

• y = x/3 + 4/3

What is the slope of the inverse function in its simplified form?

• 3

• 4/3

• x + 4

• 1/3