Math Problem Statement

Use the function values for f and g shown in the table to evaluate (f ∘ g)(-1).

Solution

The given problem asks to evaluate (fg)(1)(f \circ g)(-1), which represents the composition of the functions ff and gg, evaluated at 1-1.

Steps to solve:

  1. Find g(1)g(-1):
    From the table, look at the value of g(x)g(x) when x=1x = -1.
    g(1)=2g(-1) = -2

  2. Find f(g(1))f(g(-1)):
    Now that we know g(1)=2g(-1) = -2, we need to find f(2)f(-2). Look at the value of f(x)f(x) when x=2x = -2.
    f(2)=9f(-2) = 9

Thus, (fg)(1)=f(g(1))=f(2)=9(f \circ g)(-1) = f(g(-1)) = f(-2) = 9.

The final answer is 9.

Would you like any further details or explanations on this process?

Here are 5 related questions:

  1. How do we evaluate a composition of two functions in general?
  2. What happens when we reverse the composition, i.e., (gf)(x)(g \circ f)(x)?
  3. What is the domain of a composite function?
  4. How does function composition differ from simple multiplication of functions?
  5. Can a composite function be undefined? Under what conditions?

Tip: When dealing with composite functions, always evaluate the inner function first, then use its result to evaluate the outer function.

Ask a new question for Free

By Image

Drop file here or Click Here to upload

Math Problem Analysis

Mathematical Concepts

Function Composition
Algebra

Formulas

(f ∘ g)(x) = f(g(x))

Theorems

Function Composition Rule

Suitable Grade Level

Grades 9-12