Is (f+g)(x) the same as f(x)+g(x)?
Yes—that is the definition of function addition.
Function Operations Calculator
For linear f and g, compute (f±g)(x), (fg)(x), or (f/g)(x) at a chosen x.
Enter f, g, operation, and x
f(x)=ax+b, g(x)=cx+d. Choose an operation and evaluation point.
About this calculator
How to use Function Operations Calculator, plus the formulas and logic behind the results.
Tool description
Function arithmetic combines outputs pointwise: (f+g)(x)=f(x)+g(x), and similarly for −, ·, and ÷ (where g(x)≠0).
How to use
- Enter coefficients for f and g.
- Choose add, subtract, multiply, or divide.
- Enter the evaluation point x.
- Select Calculate to view the numeric result and simplified expression when linear.
Formulas & reference
(f + g)(x) = f(x) + g(x)(f − g)(x) = f(x) − g(x)(f · g)(x) = f(x) · g(x)(f / g)(x) = f(x) / g(x), g(x) ≠ 0
Notes
- Sum/difference of linears is linear
- Product is generally quadratic
- Quotient is rational
- Always check g(x) ≠ 0 for division
Calculation logic
Evaluates both linears at x, applies the selected operation, and for ± reports the combined linear formula.
Division fails when g(x) = 0. Products of linears are quadratic in general.
Function Operations Calculator FAQ
Common questions about this calculator and how to use the results.
When is division undefined?
Whenever g(x) = 0 at the evaluation point.
Why is the product not linear?
Multiplying two degree-1 polynomials yields degree 2.
Can coefficients be negative?
Yes.
Do I need the symbolic form?
The tool shows both the value at x and a simplified expression when helpful.
How is this different from composition?
Operations combine outputs at the same x; composition feeds one output into the other function.