**Related Pages**

Functions

Graphs Of Functions

More Lessons for Algebra

Math Worksheets

In these lessons, 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, stands for the domain set.

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

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

The following diagram shows what is function notation. Scroll down the page for more examples and solutions of function notations.

**Example:**

Given f(x) = x^{2} + 3x – 1, find

a) f(1)

b) f(–1)

c) f(a)

d) f(x – 1)

**Solution:**

a) f(1) = (1)^{2} + 3(1) – 1 = 3

b) f(–1) = (–1)^{2} + 3(–1) – 1 = –3

c) f(a) = a^{2} + 3a – 1

d) f(x – 1) = (x – 1)^{2} + 3(x – 1) – 1

= x^{2} – 2x + 1 + 3x – 3 – 1 = x^{2} + x –3

**Example:**

Give g(x) = x^{2} + 2, find

a) g(a + b)

b) g(x^{2})

**Solution:**

a) g(a + b) = (a + b)^{2} + 2

= a^{2} + 2ab + b^{2} + 2

b) g(x^{2}) = (x^{2})^{2} + 2 = x^{4} + 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**

How to use the function Notation?

A basic description of function notation and a few examples involving function notation.

Example:

If g(t) = t^{2} - 2t + 1

- g(3t)
- 5g(-1)
- solve g(t) = 1

If f(x) = 5x -2, h(x) = x^{2} - 3f(x)
- f(2x - 1)
- -f(a)
- Solve f(-x) = h(x) + 2

Try the free Mathway calculator and
problem solver below to practice various math topics. Try the given examples, or type in your own
problem and check your answer with the step-by-step explanations.

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