Finding Inverses of Functions

The video tutorial explains how to find the inverse of a function algebraically through a series of steps. It covers four examples: a linear function, a linear function with fractions, a cubic function, and a square root function. The process involves replacing function notation, switching variables, and solving for the inverse. The tutorial also hints at checking the inverse using function composition, which will be covered in a subsequent lesson.

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

• Check the inverse using composition

• Replace function notation with y

• Solve for y

• Switch the x and y variables

In the example of the linear function, what is the inverse of f(x) = 4x + 5?

• f^(-1)(x) = 4x - 5

• f^(-1)(x) = (x - 5) / 4

• f^(-1)(x) = (x + 5) / 4

• f^(-1)(x) = 4(x - 5)

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

• Replace y with inverse notation

• Solve for y

• Check the inverse using composition

• Switch x and y

What is the purpose of checking the inverse function using composition?

• To verify the inverse simplifies to y

• To check if the inverse is a quadratic function

• To ensure the inverse simplifies to x

• To confirm the inverse is a linear function

In the example with fractions, what is the inverse of G(x) = 1/3y + 25?

• G^(-1)(x) = 3x + 25

• G^(-1)(x) = x/3 - 25

• G^(-1)(x) = 3x - 25

• G^(-1)(x) = x/3 + 25

How do you find the inverse of a cubic function like H(x) = 8x^3 - 1?

• All of the above

• Switch x and y, then solve for y

• Take the cube root of both sides

• Add 1 to both sides, then divide by 8

In the example with a cubic function, what is the cube root of 8?

• 4

• 3

• 2

• 1

In the example with fractions, what is the result of multiplying both sides by 3?

• It squares the equation

• It adds a fraction

• It cubes the equation

• It eliminates the fraction

What is the inverse of a function with a square root, such as f(x) = √(x - 4) + 3?

• f^(-1)(x) = √(x + 4) - 3

• f^(-1)(x) = (x + 3)^2 - 4

• f^(-1)(x) = (x - 3)^2 + 4

• f^(-1)(x) = √(x - 4) - 3

What operation is used to eliminate a square root when finding an inverse?

• Cubing

• Addition

• Subtraction

• Squaring