Math Problem Statement

f(x)=x+3 g(x)x-2 find (f + g)

Solution

To find (f+g)(x)(f + g)(x), we need to add the two functions f(x)f(x) and g(x)g(x).

Given:

  • f(x)=x+3f(x) = x + 3
  • g(x)=x2g(x) = x - 2 (I assume there is a typo, and this is the correct expression for g(x)g(x)).

Now, let's calculate (f+g)(x)(f + g)(x):

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

(f+g)(x)=(x+3)+(x2)(f + g)(x) = (x + 3) + (x - 2)

Simplifying the right-hand side:

(f+g)(x)=x+x+32=2x+1(f + g)(x) = x + x + 3 - 2 = 2x + 1

So, (f+g)(x)=2x+1(f + g)(x) = 2x + 1.

Would you like more details or further clarification?

Here are some related questions:

  1. What is (fg)(x)(f - g)(x) for the given functions?
  2. How would you compute (fg)(x)(f \cdot g)(x)?
  3. What is f(x)g(x)\frac{f(x)}{g(x)} for these functions?
  4. Can you find the composite function f(g(x))f(g(x))?
  5. What happens if you graph both functions f(x)f(x) and g(x)g(x)?

Tip: Adding functions simply means adding their corresponding outputs for each value of xx.

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Math Problem Analysis

Mathematical Concepts

Algebra
Function Addition

Formulas

(f + g)(x) = f(x) + g(x)
f(x) = x + 3
g(x) = x - 2

Theorems

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Suitable Grade Level

Grades 6-8