Math Problem Statement

Which TWO of the parent functions listed are inverses of each other? A.Linear B.Cubic C.Logarithmic D.Square Root E.Exponential F.Rational

Solution

The two parent functions that are inverses of each other are:

C. Logarithmic and E. Exponential.

Explanation:

  • The Exponential function (e.g., y=axy = a^x) is the inverse of the Logarithmic function (e.g., y=loga(x)y = \log_a(x)).
  • These functions are inverse because the exponential function "undoes" the logarithm and vice versa. Specifically, y=loga(x)y = \log_a(x) means x=ayx = a^y, which is the definition of the exponential function.

Would you like more details on this concept, or do you have any other questions?

Here are five related questions you might find useful:

  1. What is the general form of the exponential function?
  2. How do you find the inverse of a function?
  3. What is the relationship between the base of an exponential function and its inverse logarithm?
  4. Can you graph an exponential function and its logarithmic inverse?
  5. What are other examples of inverse function pairs?

Tip: When graphing inverse functions, the graph of one function is a reflection of the other over the line y=xy = x.

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Math Problem Analysis

Mathematical Concepts

Functions
Inverse Functions
Logarithmic Functions
Exponential Functions

Formulas

Exponential function: y = a^x
Logarithmic function: y = log_a(x)

Theorems

Inverse Function Theorem
Exponential and Logarithm Inverse Property

Suitable Grade Level

Grades 9-12