Math Problem Statement

​(e) Find

​(fplus+​g)(3​).

​(fplus+​g)(3​)equals=enter your response here

​(Type an exact​ answer, using radicals as needed. Use integers or fractions for any numbers in the​ expression.)

Solution

To solve (f+g)(3)(f + g)(3), you need to know the functions f(x)f(x) and g(x)g(x).

The process would be as follows:

  1. Define f(x)f(x) and g(x)g(x).
  2. Add the two functions: (f+g)(x)=f(x)+g(x)(f + g)(x) = f(x) + g(x).
  3. Substitute x=3x = 3 into the equation.
  4. Simplify the expression to get the final answer.

If you provide the expressions for f(x)f(x) and g(x)g(x), I can proceed with the solution.

Would you like to clarify the functions, or have any questions?


Here are 5 follow-up questions that might help you understand this better:

  1. What are the exact forms of f(x)f(x) and g(x)g(x)?
  2. What happens when you combine two functions algebraically?
  3. How do you simplify expressions involving radicals?
  4. Can this approach be used with any real numbers for xx?
  5. What does function composition mean in comparison to function addition?

Tip: When dealing with radicals, simplify them as much as possible before combining terms.

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Math Problem Analysis

Mathematical Concepts

Algebra
Function Addition
Substitution
Simplification

Formulas

(f + g)(x) = f(x) + g(x)

Theorems

Addition of Functions
Substitution in Functions

Suitable Grade Level

Grades 9-12