Finding Inverses of Functions

This video tutorial covers the concept of inverse functions, explaining the steps to determine the inverse of a given function. It provides three examples: finding the inverse of x - 3, 4x + 5, and a fractional function. The video concludes with practice problems for viewers to solve.

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

• Solve for x in terms of y

• Switch x and y

• Multiply by the reciprocal

• Replace f(x) with y

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

• f^(-1)(x) = 3 - x

• f^(-1)(x) = x - 3

• f^(-1)(x) = -x + 3

• f^(-1)(x) = x + 3

What is the inverse of f(x) = x - 3?

• f^(-1)(x) = x - 3

• f^(-1)(x) = x + 3

• f^(-1)(x) = -x + 3

• f^(-1)(x) = 3 - x

What operation is performed to isolate x in the equation y = 4x + 5?

• Add 5 to both sides

• Divide both sides by 4

• Multiply both sides by 4

• Subtract 5 from both sides

What is the inverse of the function f(x) = 4x + 5?

• f^(-1)(x) = (x - 5) / 4

• f^(-1)(x) = 4x - 5

• f^(-1)(x) = 5x - 4

• f^(-1)(x) = (x + 5) / 4

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

• f^(-1)(x) = 5x - 4

• f^(-1)(x) = (x + 5) / 4

• f^(-1)(x) = 4x - 5

• f^(-1)(x) = (x - 5) / 4

In the rational function example, what is the first step after replacing f(x) with y?

• Add 3 to both sides

• Divide by 2

• Subtract 5 from both sides

• Cross-multiply to eliminate the fraction

What is the inverse of the function f(x) = (2x + 5) / (x - 3)?

• f^(-1)(x) = (5x + 3) / (2 - x)

• f^(-1)(x) = (3x + 5) / (x - 2)

• f^(-1)(x) = (2x - 5) / (x + 3)

• f^(-1)(x) = (5 + 3x) / (x - 2)

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

• Switch x and y

• Replace y with x

• Solve for y

• Simplify the equation

Which of the following is NOT a step in finding the inverse of a function?

• Solve for x in terms of y

• Replace f(x) with y

• Replace y with x

• Multiply both sides by x