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:
- Exponential and Logarithmic functions.
Here’s why:
- The exponential function typically has the form .
- The logarithmic function typically has the form , where 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:
- What is the inverse of a quadratic function?
- How do you find the inverse of a cubic function?
- Can linear and rational functions ever be inverses of each other?
- What are the properties of inverse functions in general?
- How do you graph exponential and logarithmic functions as inverses?
Tip: To verify if two functions are inverses, compose them (i.e., and ) and check if the result is .
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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
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