Tuesday, October 19, 2010

How to find vertices, edges and faces of a prism given the sides or base?

1) To find the number of vertices, edges and faces of any prism given the number of sides (or) base, use this formula:

a) vertices of a prism = 2n
b) edges of a prism = 3n
c) faces of a prism = n + 2
where n is the number of sides of a prism

Examples:
Find the number of vertices, edges and faces of a hexagonal prism.

We know that a hexagon has 6 sides (n), therefore
vertices = 2n ==> 2 * 6 = 12
edges = 3n ==> 3 * 6 = 18
faces = n + 2 ==> 6 + 2 = 8

INVERSE OF A FUNCTION

To find the inverse ( f^-1)(x) of a function f(x); follow the following steps:
Example: Find the inverse of
y = 1-2x

1) Write the original equation.
y = 1-2x

2) Solve it in terms of x.
y = 1 -2x
-2x = -1 + y
x = (1-y)/2

3) Interchange y and x in the result of step 2.

x = (1-y)/2 ==> y = (1-x)/2

4) The inverse function f^-1(x) of f(x) = 1 -2x
is therefore f^-1(x) = (1-x)/2