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

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 \( y = a^x \).
- The **logarithmic function** typically has the form \( y = \log_a(x) \), where \( a \) 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., \( f(g(x)) \) and \( g(f(x)) \)) and check if the result is \( x \).

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

Learn how exponential and logarithmic functions are inverses of each other. Explore key mathematical concepts such as inverse functions and the relationship between y = a^x and y = log_a(x). Suitable for high school students in Grades 9-12.

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