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 , let's first break down the two given functions and then add them together.
Given:
Now, we add the two functions:
Combining like terms:
Simplifying:
Thus, the result of is:
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:
- Find given the same functions.
- Calculate , the composition of the two functions.
- What is the derivative of ?
- Solve .
- Find the roots of .
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