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.

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

These two functions undo each other because:

  • If y=axy = a^x, then taking the logarithm gives loga(y)=x\log_a(y) = x.
  • If y=loga(x)y = \log_a(x), then exponentiating gives ay=xa^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))=xf(g(x)) = g(f(x)) = x.

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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