Analyze paired functions for structured wellness math practice. Check sums, differences, products, and quotients instantly. Export clean results and examples for calm daily study.
Use quadratic form: ax² + bx + c for both functions.
| Example | f(x) | g(x) | x | (f+g)(x) | (f-g)(x) | (fg)(x) | (f/g)(x) |
|---|---|---|---|---|---|---|---|
| Sample A | x² + 2x + 1 | x² - x + 3 | 2 | 2x² + x + 4; value 14 | 3x - 2; value 4 | x^4 + x^3 + 2x^2 + 5x + 3; value 45 | (x² + 2x + 1)/(x² - x + 3); value 1.8 |
| Sample B | 2x² + x - 4 | x² + 3x + 2 | 1 | 3x² + 4x - 2; value 5 | x² - 2x - 6; value -7 | 2x^4 + 7x^3 + 3x^2 - 10x - 8; value -6 | (2x² + x - 4)/(x² + 3x + 2); value -0.166667 |
Sum of functions: (f + g)(x) = f(x) + g(x)
Difference of functions: (f - g)(x) = f(x) - g(x)
Product of functions: (fg)(x) = f(x) × g(x)
Quotient of functions: (f / g)(x) = f(x) / g(x), where g(x) ≠ 0
Quadratic form used here: f(x) = ax² + bx + c and g(x) = dx² + ex + f
This f+g f-g fg f/g calculator helps you compare two functions fast. It works well for study, journaling models, and structured practice. You can define both functions, test one x value, and review the combined result. This makes symbolic math easier to read. It also reduces manual algebra mistakes.
In mental health planning, people often compare two changing patterns. One function may represent stress intensity. Another may represent recovery support. The sum can show total load. The difference can show balance. The product can show interaction strength. The quotient can show proportional change across one chosen input.
The sum of functions combines both trends into one expression. That is helpful when you want a wider view. The difference shows separation between patterns. It can reveal gaps, overlap, or changing direction. For reflective worksheets, this helps users inspect how two modeled factors relate at the same point.
The product of functions is useful when one trend amplifies another. It creates a richer polynomial result. The quotient is useful when comparison by ratio matters. This is common in performance review, score analysis, and self-monitoring models. The calculator also warns you when division becomes undefined.
This page returns the result above the form for easier review. You can inspect function expressions and evaluated values together. The responsive input area keeps the calculator organized on large and small screens. The CSV export supports records and worksheets. The PDF option helps save or print a clean report.
Students can use this tool to check algebra steps. Tutors can use it for demonstrations. Analysts can use it when building simple wellness scoring examples. The page also includes formulas, an example data table, and direct instructions. That makes the calculator useful for both quick checks and guided learning.
It computes the sum, difference, product, and quotient of two functions. It also evaluates every result at the selected x value.
This version uses quadratic input for both functions. You can still enter linear or constant functions by setting unused coefficients to zero.
The quotient becomes undefined. The calculator shows that clearly, because division by zero is not allowed in function operations.
Yes. The inputs accept decimals, negative numbers, and whole numbers. That makes the tool useful for classroom work and modeled scoring systems.
Symbolic results show the full algebraic expression. Numeric results show the exact value at your chosen x input. Seeing both improves verification.
No. It fits algebra, statistics, journaling models, education, and any situation where two functions must be combined and checked quickly.
The CSV file includes the original functions, the selected x value, the four operation expressions, and the evaluated outputs for quick recordkeeping.
The PDF button opens your browser print flow. You can then save the visible result section as a PDF document.