Mathematical Formulas for Industrial and Mechanical Engineering

5.1 Functions and Their Graphs

G

A function f(x) is a relation between a set of inputs (range) and a set of permissible outputs

(domain) with the property that each input is related to exactly one output. Example of

function: f(x) 5 5x. Example of a non function: f(x) 56Ox.

G

Even function: f(2x) 5 f(x). Example: f(x) 5 x

2

.

G

Odd function: f(2x) 52f(x). Example: f(x) 5 x

3

.

G

Periodic function: f(x 1 nT) 5 f(x). Example: f(x) 5 sin(x).

G

Inverse function: y 5 f(x) is any function, x 5 g(y)ory 5 f

2l

(x) is its inverse function.

Example: f(x) 5 2x 1 3!f

21

(y) 5 (y 2 3)/2.

G

Composite function: y 5 f(u), u 5 g(x), y 5 f (g(x)) is a composite function.

G

Linear funct ...