Math Problem Statement

Evaluate g(h(-3)) using the tables for functions g and h.

Solution

To evaluate g(h(3))g(h(-3)), we will need to follow these steps:

  1. Find h(3)h(-3): From the second table: h(3)=2h(-3) = 2

  2. Find g(h(3))=g(2)g(h(-3)) = g(2): Now use the value h(3)=2h(-3) = 2 in the first table to find g(2)g(2): g(2)=7g(2) = 7

Thus, g(h(3))=7g(h(-3)) = 7.

Would you like more details on any part of the process?

Here are five questions to expand your understanding:

  1. What is the composition of functions and how is it used in this problem?
  2. How would the process change if the tables were given as equations instead of values?
  3. Can the values of g(x)g(x) and h(x)h(x) be used to deduce the formulas of the functions?
  4. What happens if g(x)g(x) and h(x)h(x) have domain restrictions? How would that affect the evaluation?
  5. How can function composition be applied in real-world contexts?

Tip: When composing functions, always apply the inner function first and then the outer function for correct evaluation.

Ask a new question for Free

By Image

Drop file here or Click Here to upload

Math Problem Analysis

Mathematical Concepts

Function Composition
Function Evaluation

Formulas

g(h(x)) where g and h are functions

Theorems

Function Composition Theorem

Suitable Grade Level

Grades 9-10