Math Problem Statement

Given that f, of, x, equals, x, squared, minus, 11, x, plus, 18f(x)=x 2 −11x+18 and g, of, x, equals, x, minus, 2g(x)=x−2, find f, of, x, plus, g, of, xf(x)+g(x) and express the result as a polynomial in simplest form

Solution

To find f(x)+g(x)f(x) + g(x), let's first break down the two given functions and then add them together.

Given: f(x)=x211x+18f(x) = x^2 - 11x + 18 g(x)=x2g(x) = x - 2

Now, we add the two functions:

f(x)+g(x)=(x211x+18)+(x2)f(x) + g(x) = (x^2 - 11x + 18) + (x - 2)

Combining like terms:

f(x)+g(x)=x211x+x+182f(x) + g(x) = x^2 - 11x + x + 18 - 2

Simplifying:

f(x)+g(x)=x210x+16f(x) + g(x) = x^2 - 10x + 16

Thus, the result of f(x)+g(x)f(x) + g(x) is: f(x)+g(x)=x210x+16f(x) + g(x) = x^2 - 10x + 16

This is the polynomial in its simplest form.

Would you like further details or have any other questions?

Here are 5 related questions for further practice:

  1. Find f(x)g(x)f(x) - g(x) given the same functions.
  2. Calculate f(g(x))f(g(x)), the composition of the two functions.
  3. What is the derivative of f(x)+g(x)f(x) + g(x)?
  4. Solve f(x)+g(x)=0f(x) + g(x) = 0.
  5. Find the roots of f(x)+g(x)f(x) + g(x).

Tip: Always combine like terms carefully when adding or subtracting polynomials to avoid mistakes.

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Math Problem Analysis

Mathematical Concepts

Algebra
Polynomials
Function Addition

Formulas

f(x) + g(x) = (f(x)) + (g(x))
Combining like terms: ax^2 + bx + c

Theorems

Polynomial Simplification

Suitable Grade Level

Grades 8-10