Inverse Functions: Logarithmic and Exponential

In this video, Amal Kumar explains how to find the inverse of exponential functions, revealing that the inverse is a logarithmic function. The video demonstrates writing the inverse in both exponential and logarithmic forms using examples such as y = 3^x and y = 10^x. The process involves swapping x and y, and applying logarithms to both sides. The video concludes with a summary of the methods discussed.

What is the inverse of an exponential function?

• A quadratic function

• A linear function

• A logarithmic function

• A trigonometric function

In how many ways can the inverse of an exponential function be expressed?

• Four ways

• Three ways

• Two ways

• One way

What is the exponential form of the inverse of y = 3^x?

• x = y^3

• y = x^3

• y = 3^x

• x = 3^y

What is the logarithmic form of the inverse of y = 3^x?

• x = log_y(3)

• y = log_x(3)

• x = log_3(y)

• y = log_3(x)

Which base is used in the logarithmic form of the inverse of y = 3^x?

• Base 10

• Base 3

• Base 2

• Base e

What is the key step in finding the logarithmic form of an inverse function?

• Multiplying both sides by the base

• Adding the base to both sides

• Taking the logarithm of both sides

• Subtracting the base from both sides

What is the exponential form of the inverse of x = 1/10^y?

• y = 10^x

• y = 1/10^x

• x = 1/10^y

• x = 10^y

What is the logarithmic form of the inverse of x = 1/10^y?

• y = log_10(x)

• x = log_y(10)

• y = log_x(10)

• x = log_10(y)

What is the base used in the logarithmic form of the inverse of x = 1/10^y?

• Base e

• Base 2

• Base 3

• Base 10

What is the relationship between exponential and logarithmic functions?

• They are unrelated

• They are inverses of each other

• They are the same

• They are both quadratic