Math Problem Statement

Sum of functions f(x) = 6x^2 + 2x + 3 and g(x) = x^2 - 3x + 5

Solution

The image contains the mathematical functions f(x)=6x2+2x+3f(x) = 6x^2 + 2x + 3 and g(x)=x23x+5g(x) = x^2 - 3x + 5, and the operation is the sum of these two functions.

Sum of the Functions:

To find (f+g)(x)(f + g)(x), you add the two functions f(x)f(x) and g(x)g(x):

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

Now, substitute the expressions for f(x)f(x) and g(x)g(x):

(f+g)(x)=(6x2+2x+3)+(x23x+5)(f + g)(x) = (6x^2 + 2x + 3) + (x^2 - 3x + 5)

Combine like terms:

  1. 6x2+x2=7x26x^2 + x^2 = 7x^2
  2. 2x3x=x2x - 3x = -x
  3. 3+5=83 + 5 = 8

Thus, the resulting function after addition is:

(f+g)(x)=7x2x+8(f + g)(x) = 7x^2 - x + 8

Would you like further details or explanations?

Here are 5 related questions for practice:

  1. What is the result of f(x)g(x)f(x) - g(x)?
  2. Can you find f(x)×g(x)f(x) \times g(x)?
  3. What is the derivative of f(x)f(x)?
  4. What is the solution to f(x)=0f(x) = 0?
  5. How do you find the quotient f(x)g(x)\frac{f(x)}{g(x)}?

Tip: When adding polynomials, always group and combine like terms (terms with the same degree).

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Math Problem Analysis

Mathematical Concepts

Functions
Polynomial Addition

Formulas

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

Theorems

Polynomial addition rule

Suitable Grade Level

Grades 8-10