Inverse Functions and Logarithmic Properties

The video tutorial explains how to find the inverse of exponential functions, which are logarithmic functions. It provides step-by-step instructions and examples, including the use of logarithms and the change of base formula. The tutorial also covers natural logarithms and the special case of base e, demonstrating how to solve for inverse functions in these contexts.

What is the inverse of an exponential function?

• A quadratic function

• A trigonometric function

• A logarithmic function

• A polynomial function

When finding the inverse of f(x) = 3^x + 5, what is the first step?

• Replace f(x) with y

• Take the derivative

• Switch x and y

• Add 5 to both sides

In the equation log(x - 5) = y * log(3), how do you isolate y?

• Multiply both sides by log(3)

• Divide both sides by log(3)

• Add log(3) to both sides

• Subtract log(3) from both sides

What property of logarithms allows you to move the exponent to the front?

• Product rule

• Change of base formula

• Quotient rule

• Power rule

What happens to the base in a logarithm when using the change of base formula?

• It is halved

• It is squared

• It becomes the denominator

• It becomes the numerator

What is the base of a natural logarithm?

• 2

• 10

• e

• 3

What is the approximate value of e?

• 1.61803

• 3.14159

• 1.41421

• 2.71828

In the equation ln(4 - 0.5x) = 5y * ln(e), what is the value of ln(e)?

• 0

• 1

• 5

• e

How do you isolate y in the equation 5y = ln(4 - 0.5x)?

• Divide both sides by 5

• Multiply both sides by 5

• Subtract 5 from both sides

• Add 5 to both sides

What is the inverse function of f(x) = 8 - 2e^(5x)?

• ln(8 - 5x)

• ln(5x - 2)

• ln(8 - 2x)

• ln(4 - 0.5x)