Function Operations
Compute (f+g)(x), (f−g)(x), (f·g)(x) and (f/g)(x) for two expressions at a given x.
Inputs
(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
Values used
f(x) = x^2 + 1; g(x) = x - 3; x value = 5
Sum
(f+g)(x) = f(x) + g(x)
Quotient
(f/g)(x) = f(x) / g(x), g(x) ≠ 0
(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
How it works
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
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)).