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

Answer: 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)

$= 49 + 4$

$= 53$

Answer: 53