Functions f(x)

## Functions f(x)

A function can be written as f(x), which is shorthand for the function of x is such that followed by an expression for the function eg f(x) = 2x + 4. The right hand side states what will be done to x: multiply by 2 and add 4.

A function is written with a single letter (normally f) followed by a variable (normally x) in brackets on the left hand side of the equation sign; and an expression (the function to be applied to that variable) on the right hand side.

When a function is evaluated, replace the variable with the number: using the above function,

f(3) = 2 xx 3 + 4 = 10 or

f(-5) = 2 xx -5 + 4 = -6

Sometimes the function may be written slightly differently with a colon and an arrow:

x: → 2x + 4 or even as x ↦ 2x + 4.

## Example 1

f(x) is defined as f(x) = 3x^2 + 2.

What is the value of f(7)?

f(x) = 3x^2 + 2

f(7) = 3(7)^2 + 2

= 3 x 49 + 2

=149

## Example 2

Given a function f(x) = x^2 + 4, find the value of f(7).

f(x) = x^2 + 4

f(7) = 7^2 + 4 (Replace x with 7)

= 49 + 4

= 53