Function Operations
Compute (f+g)(x), (f−g)(x), (f·g)(x) and (f/g)(x) for two expressions at a given x.
About Function Operations
Function operations combine two functions pointwise: (f+g)(x) = f(x)+g(x), (f−g)(x) = f(x)−g(x), (f·g)(x) = f(x)·g(x), and (f/g)(x) = f(x)/g(x) (when g(x)≠0). This calculator evaluates all four operations at a given x value.
Formulas
Sum
(f+g)(x) = f(x) + g(x)
- f
- First function
- g
- Second function
Quotient
(f/g)(x) = f(x) / g(x), g(x) ≠ 0
- f
- Numerator function
- g
- Denominator function
Worked example
With the default values below, Function Operations returns (f+g)(x) of 28.00000000. Change any input above and every figure here is recalculated in your browser.
Inputs used
- f(x)
- x^2 + 1
- g(x)
- x - 3
- x value
- 5
Results
- (f+g)(x)
- 28.00000000
- (f−g)(x)
- 24.00000000
- (f·g)(x)
- 52.00000000
- (f/g)(x)
- 13.00000000
- f(x)
- 26.00000000
- g(x)
- 2.00000000
Step by step
- 1Values used
- 2Sum
- 3Quotient
- 4(f+g)(x)= 28.00000000
- 5(f−g)(x)= 24.00000000
- 6(f·g)(x)= 52.00000000
- 7(f/g)(x)= 13.00000000
- 8f(x)= 26.00000000
- 9g(x)= 2.00000000
Assumptions and limits
- The result is derived only from the 3 inputs listed above. Anything not among them is not part of the calculation.
- In particular, this calculator does not take inflation, tax, fees or charges or compounding frequency into account.
- Figures are rounded for display to 8 decimal places, so totals built from several rounded parts can differ slightly from the unrounded arithmetic.
How these calculators are built and tested is described on the Methodology page. If a figure looks wrong, please report it.
Frequently Asked Questions
What if g(x) = 0 for the division?
The quotient (f/g)(x) is undefined when g(x) = 0. In that case, the quotient field will be empty.
Are these the same as composition?
No — function operations combine outputs pointwise (+, −, ×, ÷). Composition feeds one function's output as the other's input: f(g(x)).