Activities

Objectives

• Students will recognize the function g(x) =  log_x(x) as the inverse of f(x)=b^x where b > 0 and b ≠ 1
• Students will apply this inverse relationship and solve simple logarithmic equations

Vocabulary

• Exponential function
• Logarithmic function
• One-to-one function
• Inverse function
• Domain and range

About the Lesson

This lesson involves the one-to-one function f(x)=b^x. In acknowledging the existence of its inverse, students will:

• Use the domain and range of f(x) to determine the domain and range of f^-1(x).
• Interpret the graph of f^-1(x) as the reflection of f(x) across the line y = x.
• Use this inverse relationship to write an equation for the graph of the inverse.
• Recognize the logarithmic notation needed to define the inverse function.
• Use the inputs and outputs of two inverse functions to complete a table.
  
  As a result, students will:
• Solve simple logarithmic equations and verify solutions using the corresponding exponential equations.