Math Problem Statement
Given that f, of, x, equals, x, squared, minus, 11, x, plus, 30f(x)=x 2 −11x+30 and g, of, x, equals, x, minus, 5g(x)=x−5, find left parenthesis, f, minus, g, right parenthesis, left parenthesis, x, right parenthesis(f−g)(x) and express the result as a polynomial in simplest form. '
Solution
We are asked to find , which means we need to subtract the function from .
Given:
Now, let's compute : Substitute and :
Distribute the negative sign:
Now, combine like terms:
Thus, the result is:
Would you like more details or have any questions?
Here are 5 related questions you might find useful:
- What is the result of adding and instead of subtracting?
- How can we find the product of and ?
- How do you find the roots of the polynomial ?
- What is the graphical interpretation of subtracting two functions?
- How do you find the vertex of the quadratic function ?
Tip: When subtracting functions, always distribute the negative sign carefully to avoid mistakes with signs in each term.
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Math Problem Analysis
Mathematical Concepts
Algebra
Polynomials
Function Subtraction
Formulas
(f - g)(x) = f(x) - g(x)
Quadratic Polynomial: ax^2 + bx + c
Theorems
-
Suitable Grade Level
Grades 9-11
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