Math Problem Statement

Evaluate each expression using the graphs of y equals f left parenthesis x right parenthesis and y equals g left parenthesis x right parenthesis shown below. ​a) left parenthesis g circle f right parenthesis left parenthesis 5 right parenthesis ​b) left parenthesis g circle f right parenthesis left parenthesis 0 right parenthesis ​c) left parenthesis f circle g right parenthesis left parenthesis 3 right parenthesis ​d) left parenthesis f circle g right parenthesis left parenthesis 4 right parenthesis -4 -2 2 4 6 8 10 -6 -4 -2 2 4 6 8 x y y = g(x) y = f(x)

Solution

It appears that you are asking for the evaluation of composite functions (g∘f)(x)(g \circ f)(x) and (f∘g)(x)(f \circ g)(x), given the graphs of y=f(x)y = f(x) and y=g(x)y = g(x). However, I don't have access to the graphs you mentioned.

Could you provide a brief description or a picture of the graphs? This will help me extract the function values and proceed with the calculations.

Once I have that information, I'll be able to help you evaluate:

  1. (g∘f)(5)(g \circ f)(5)
  2. (g∘f)(0)(g \circ f)(0)
  3. (f∘g)(3)(f \circ g)(3)
  4. (f∘g)(4)(f \circ g)(4)

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Math Problem Analysis

Mathematical Concepts

Function Composition
Graphical Analysis
Function Evaluation

Formulas

(g ∘ f)(x) = g(f(x))
(f ∘ g)(x) = f(g(x))

Theorems

Function Composition Theorem

Suitable Grade Level

Grades 9-12

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