A function is a relation that assigns to each input value exactly one output value. Like numbers and polynomials we can add, subtract, multiply and divide functions which results into a new function. Below are the rules to perform these operations on functions.
Let f(x) and g(x) be two functions:
Addition
We can add two functions as:
(f + g)(x) = f(x) + g(x)
Example:
f(x) = 2x2 + 3x – 4 and g(x) = 2x + 3
(f + g)(x) = (2x2 + 3x – 4) + (2x + 3)
= 2x2 + 5x – 1
Subtraction
We can subtract two functions as:
(f – g)(x) = f(x) – g(x)
Example:
f(x) = 2x2 + 3x – 4 and g(x) = 2x + 3
(f – g)(x) = (2x2 + 3x – 4) – (2x + 3)
= 2x2 + x – 7
Multiplication
(f•g)(x) = f(x)•g(x)
Example:
f(x) = 3x – 5 and g(x) = x
(f•g)(x) = (3x – 5)•(x)
= 3x2 – 5x
Division
(f/g)(x) = f(x)/g(x)
Example:
f(x) = 3x2 + 4x – 3 and g(x) = x
(f/g)(x) = (3x2 + 4x – 3)/x
= 3x + 4 – 3/x
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