Math Problem Statement

Do question 8e

Use the functions g(x) = x + 3 and h(x) = 2x - 4 to find g^{-1} ∘ h^{-1}

Solution

For part 8(e), the composition of the inverse functions g1h1g^{-1} \circ h^{-1} results in the function:

g1(h1(x))=x3g^{-1}(h^{-1}(x)) = x - 3

Would you like more details or further clarifications? Here are five related questions to deepen your understanding:

  1. How do you generally find the inverse of a function?
  2. What are the properties of composite functions?
  3. How can you verify if two functions are inverses of each other?
  4. What happens when you compose a function with its inverse?
  5. Why is it important for a function to be one-to-one to have an inverse?

Tip: When finding the inverse of a function, swap xx and yy, then solve for yy.

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Math Problem Analysis

Mathematical Concepts

Inverse Functions
Function Composition

Formulas

Inverse function formula: If f(x) = y, then f^{-1}(y) = x
Function composition: (g ∘ h)(x) = g(h(x))

Theorems

Inverses of composite functions
One-to-one and onto functions

Suitable Grade Level

Grades 10-12