What is Algebra of Functions?
Algebra of functions means combining two functions using mathematical operations
just like we combine numbers.
Instead of adding numbers directly, we first find the value of each function
and then perform the operation.
👉 Important Idea:
First find f(x) and g(x), then apply operation.
Why Do We Use It?
- To combine two different rules into one
- To simplify expressions
- Used in higher maths like calculus
Types of Operations
1. Addition
(f + g)(x) means add outputs of both functions
(f + g)(x) = f(x) + g(x)
2. Subtraction
Subtract output of g(x) from f(x)
(f - g)(x) = f(x) - g(x)
3. Multiplication
Multiply outputs of both functions
(fg)(x) = f(x) × g(x)
4. Division
Divide output of f(x) by g(x)
(f/g)(x) = f(x) / g(x), where g(x) ≠ 0
Step-by-Step Example
Let:
Find (f + g)(2)
- Step 1: f(2) = 2² = 4
- Step 2: g(2) = 2 + 1 = 3
- Step 3: Add → 4 + 3 = 7
👉 Final Answer: (f + g)(2) = 7
Understanding with Diagram
Input goes into both functions, then outputs are combined.
Domain Important Rule
- For +, −, × → Domain = common values of both functions
- For division → g(x) ≠ 0
👉 Always check denominator in division
Key Points to Remember
- Operations are done on outputs
- First solve inside functions
- Domain can change after operation
- Division has restriction