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Function Notation

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In this lesson, we will look into the notation for functions and how to obtain the value of a function.

What is function notation?

Functions are given letter names.

The names are of the form f(x) which is read “f of x”. The letter inside the parentheses, usually x, stand for the domain set.

The entire symbol, usually f(x), stands for the range set.

The ordered-pair numbers become (x, f(x)).


Given f(x) = x2 + 3x – 1, find

a) f(1)
b) f(–1)
c) f(a)
d) f(x – 1)


a) f(1) = (1)2 + 3(1) – 1 = 3

b) f(–1) = (–1)2 + 3(–1) – 1 = –3

c) f(a) = a2 + 3a – 1

d) f(x – 1) = (x – 1)2 + 3(x – 1) – 1
= x2 – 2x + 1 + 3x – 3 – 1 = x2 + x –3


Give g(x) = x2 + 2, find

a) g(a + b)
b) g(x2)


a) g(a + b) = (a + b)2 + 2
= a2 + 2ab + b2 + 2

b) g(x2) = (x2)2 + 2 = x4 + 2

Function Notation
Throughout mathematics, we find function notation. Function notation is a way to write functions that is easy to read and understand. Functions have dependent and independent variables, and when we use function notation the independent variable is commonly x, and the dependent variable is f(x). In order to write a relation or equation using function notation, we first determine whether the relation is a function.
Function Notation - A basic description of function notation and a few examples involving function notation.

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