Function Operations

All math tools

Add, subtract, multiply, and divide two linear functions f(x) and g(x).

Input Functions

Function f(x)

f(x) multiplier (a)

f(x) constant (b)

Function g(x)

g(x) multiplier (c)

g(x) constant (d)

Operation

Operating Result

3.00x + 2.00

Resulting Rule

The result of combining both functions

Value at x = 15.00

ComplexityLinear

About this calculator

Algebra of Functions

Just like numbers, functions can be added, subtracted, multiplied, and divided to create new functions. The domain of the resulting function is usually the intersection of the domains of the two original functions, with the extra restriction that for division, the denominator function g(x) cannot be zero.

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Pro Tips

Distributive Property: When multiplying functions (f · g), remember to apply FOIL if both are binomials.
Denominator Check: When dividing functions, always look for values of x that make g(x) = 0; these are excluded from the domain.
Like Terms: When adding or subtracting, only combine terms with the same power of x.

Fun Facts

"Function composition f(g(x)) is a DIFFERENT operation, where the output of one function becomes the input for the next."
"The set of all continuous real-valued functions forms a 'Vector Space' because they follow these operation rules."
"Modern programming uses 'Higher-Order Functions' which can take other functions as arguments and combine them using these same mathematical principles."

Formula: (f ± g)(x) = f(x) ± g(x) | (fg)(x) = f(x) · g(x) | (f/g)(x) = f(x) / g(x)