Finding Inverses of Functions

The video tutorial explains how to determine the inverse of a function through four example problems. The instructor begins with a linear function, demonstrating the steps to find its inverse. The process involves substituting y for f(x), solving for x, and then expressing the inverse function. The tutorial progresses to more complex functions, including a rational function and a quadratic function, each time detailing the method to isolate x and find the inverse. The video concludes with a summary of the steps and a farewell message.

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

• Interchange x and y

• Replace y with x

• Differentiate the function

• Solve for y in terms of x

In the first problem, what is the inverse of the function f(x) = 5x - 3?

• (x - 3) / 5

• 5(x - 3)

• 5x + 3

• (x + 3) / 5

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

• Solve for x in terms of y

• Solve for y in terms of x

• Replace x with y

• Differentiate the function

In the second problem, what is the inverse of the function f(x) = 3x - 2?

• (4x + 2) / 3

• (x + 2) / 3

• (x - 2) / 3

• (4x - 2) / 3

What is the main challenge in finding the inverse of a rational function?

• Handling fractions

• Solving quadratic equations

• Differentiating the function

• Interchanging variables

In the third problem, what is the inverse of the function f(x) = (3 - 5x) / (2x + 1)?

• (3 - x) / (2x - 5)

• (3 + x) / (2x - 5)

• (3 - x) / (2x + 5)

• (3 + x) / (2x + 5)

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

• Complete the square

• Differentiate the function

• Interchange x and y

• Solve for y in terms of x

In the fourth problem, what is the inverse of the function f(x) = x^2 - 4x - 5?

• ±√(x + 9) + 2

• ±√(x - 9) - 2

• ±√(x + 9) - 2

• ±√(x - 9) + 2

What is the purpose of completing the square in finding the inverse of a quadratic function?

• To find the vertex

• To simplify the function

• To solve for x

• To make the function linear

What is the final step in finding the inverse of any function?

• Interchange x and y

• Verify the inverse

• Solve for y

• Replace y with x