Math Problem Statement

Which TWO of the parent functions listed are inverses of each other?

Which TWO of the parent functions listed are inverses of each other?

Square Root

Linear

Cubic

Logarithmic

Exponential

Rational

Solution

The two parent functions that are inverses of each other from the list provided are:

  1. Exponential and Logarithmic functions.

Here’s why:

  • The exponential function typically has the form y=axy = a^x.
  • The logarithmic function typically has the form y=loga(x)y = \log_a(x), where aa is the base of the logarithm.

These two functions undo each other’s operations. That means if you apply a logarithm to the result of an exponential function, you return to the original value, and vice versa. This satisfies the condition of being inverses.

Would you like further details or have any questions?

Here are five related questions:

  1. What is the inverse of a quadratic function?
  2. How do you find the inverse of a cubic function?
  3. Can linear and rational functions ever be inverses of each other?
  4. What are the properties of inverse functions in general?
  5. How do you graph exponential and logarithmic functions as inverses?

Tip: To verify if two functions are inverses, compose them (i.e., f(g(x))f(g(x)) and g(f(x))g(f(x))) and check if the result is xx.

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Math Problem Analysis

Mathematical Concepts

Exponential Functions
Logarithmic Functions
Inverse Functions

Formulas

Exponential function: y = a^x
Logarithmic function: y = log_a(x)
Inverse function: f(f^(-1)(x)) = x

Theorems

Inverse Function Theorem
Properties of Exponential and Logarithmic Functions

Suitable Grade Level

Grades 9-12