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


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


Rational


Linear


Square Root


Logarithmic


Exponential


Cubic

The **logarithmic** and **exponential** parent functions are inverses of each other.

1. **Exponential function**: \( y = a^x \)
2. **Logarithmic function**: \( y = \log_a(x) \)

These two functions undo each other because:

- If \( y = a^x \), then taking the logarithm gives \( \log_a(y) = x \).
- If \( y = \log_a(x) \), then exponentiating gives \( a^y = x \).

Would you like more details or examples to further clarify?

### Relative questions:
1. What are the domain and range of exponential functions?
2. How can we graph the inverse of a function?
3. What is the inverse of the cubic function?
4. How do we find the inverse of a rational function?
5. Can all functions have an inverse?

**Tip**: To check if two functions are inverses, you can compose them (both ways) and see if the result is the identity function: \( f(g(x)) = g(f(x)) = x \).

Which TWO of the parent functions listed are inverses of each other?
Rational
Linear
Square Root
Logarithmic
Exponential
Cubic

Learn about inverse functions, focusing on the relationship between logarithmic and exponential functions. Understand the key formulas and theorems behind why these two functions are inverses. Ideal for students in Grades 9-12.

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