Math Problem Statement
Solution
Let's break down the problems from your image and solve them step by step.
Given functions:
(a) Find :
We add and .
So, .
(b) Find :
We subtract from .
So, .
(c) Find :
We multiply and .
So, .
(d) Find :
We divide by .
Domain of :
The domain of a rational function excludes values of that make the denominator zero. So, we solve:
Thus, the domain is all real numbers except . In interval notation, the domain is:
Summary of Answers:
(a)
(b)
(c)
(d)
Domain:
Would you like further details on any part of these solutions?
Here are 5 related questions for practice:
- What is for different given functions?
- How would you find ?
- What happens to the domain if both and involve quadratic terms?
- How would you solve for more complex functions?
- What is the domain of when both functions have multiple variables?
Tip: When finding domains of rational functions, always check when the denominator becomes zero.
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Math Problem Analysis
Mathematical Concepts
Algebra
Function Operations
Domain of Functions
Rational Functions
Formulas
(f + g)(x) = f(x) + g(x)
(f - g)(x) = f(x) - g(x)
(fg)(x) = f(x) * g(x)
(f/g)(x) = f(x) / g(x)
Theorems
Domain Exclusion Rule for Rational Functions
Suitable Grade Level
High School (Grades 9-12)