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?
Rational
Linear
Square Root
Logarithmic
Exponential
Cubic
Solution
The logarithmic and exponential parent functions are inverses of each other.
- Exponential function:
- Logarithmic function:
These two functions undo each other because:
- If , then taking the logarithm gives .
- If , then exponentiating gives .
Would you like more details or examples to further clarify?
Relative questions:
- What are the domain and range of exponential functions?
- How can we graph the inverse of a function?
- What is the inverse of the cubic function?
- How do we find the inverse of a rational function?
- 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: .
Ask a new question for Free
By Image
Drop file here or Click Here to upload
Math Problem Analysis
Mathematical Concepts
Inverses of Functions
Exponential Functions
Logarithmic Functions
Formulas
Exponential function: y = a^x
Logarithmic function: y = log_a(x)
Theorems
Inverses of Exponential and Logarithmic Functions
Composition of Inverse Functions
Suitable Grade Level
Grades 9-12
Related Recommendation
Inverse Parent Functions: Logarithmic and Exponential Relationship
Identifying Inverse Functions: Exponential vs Logarithmic
Identifying Inverse Parent Functions: Logarithmic and Exponential
Understanding Inverses of Logarithmic and Exponential Functions
Logarithmic Function Domain and Its Inverse Exponential Range