Finding Inverses of Functions

The video tutorial explains how to find inverse functions for given one-to-one functions. It covers the concept of inverse functions, demonstrating with examples of linear and cubic functions. The process involves interchanging x and y variables and solving for y. Graphical verification is used to confirm the correctness of the inverse functions by checking symmetry across the line y = x.

What is the relationship between a function and its inverse?

• They undo each other.

• They are identical.

• They are parallel.

• They are perpendicular.

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

• Replace 'f of x' with y.

• Solve for x.

• Graph the function.

• Interchange x and y variables.

After interchanging x and y variables, what is the next step in finding the inverse of a function?

• Replace y with 'f inverse of x'.

• Graph the function.

• Interchange x and y again.

• Solve for y.

How can you write the inverse function y = (x + 5) / 3 in another form?

• y = 3x + 5

• y = x / 3 + 5 / 3

• y = (x - 5) / 3

• y = 3 / (x + 5)

What is the graphical method to verify an inverse function?

• Check if the function is continuous.

• Check if the function is differentiable.

• Graph the function and its inverse to see if they intersect at the origin.

• Graph the function and its inverse to see if they are symmetrical across the line y = x.

What is the first step in finding the inverse of the function y = 4x^3 + 9?

• Divide both sides by 4.

• Interchange x and y variables.

• Replace 'f of x' with y.

• Subtract 9 from both sides.

After interchanging x and y variables in the function y = 4x^3 + 9, what is the next step?

• Multiply both sides by 4.

• Divide both sides by 4.

• Subtract 9 from both sides.

• Add 9 to both sides.

How do you undo the cube in the equation y^3 = (x - 9) / 4?

• Multiply both sides by 3.

• Take the cube root of both sides.

• Divide both sides by 3.

• Square both sides.

What is the final form of the inverse function for y = 4x^3 + 9?

• f inverse of x = (x + 9) / 4

• f inverse of x = cube root of 2(x - 18) / 2

• f inverse of x = cube root of (x - 9) / 4

• f inverse of x = (x - 9) / 4

How can you verify the inverse function graphically?

• Graph the function and its inverse to see if they intersect at the origin.

• Graph the function and its inverse to see if they are symmetrical across the line y = x.

• Check if the function is differentiable.

• Check if the function is continuous.