Math Problem Statement
If f(x)=x 2 −2, g(x)=3x−4, and h(x)=2−4x , find (f−g)(x).
Solution
To find , you need to subtract the function from :
Given:
Now, is defined as:
Substitute the expressions for and :
Distribute the negative sign:
Simplify the expression:
So, the result is:
Let me know if you'd like more details or have any questions! Here are five related questions:
- How do you find the difference of two functions in general?
- What is the domain of the resulting function ?
- How would you find the zeros of ?
- How does subtracting functions relate to adding functions?
- How do function transformations affect the graph of ?
Tip: Always simplify the resulting expression when combining functions, especially when subtracting or adding!
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Math Problem Analysis
Mathematical Concepts
Algebra
Function Subtraction
Quadratic Functions
Linear Functions
Formulas
(f - g)(x) = f(x) - g(x)
f(x) = x^2 - 2
g(x) = 3x - 4
Theorems
Function Subtraction Property
Suitable Grade Level
Grades 8-10