What is an Inverse Function?

If you have a function called ƒ, let’s call its inverse ƒ^–1 (i.e. ƒ^–1 is the inverse function of ƒ).

By definition, the property of ƒ^–1 is that if ƒ(a)=b, then ƒ^–1(b)=a. Wikipedia (http://en.wikipedia.org/wiki/Inverse_function) has a good example:

A function ƒ and its inverse ƒ^–1. Because ƒ maps a to 3, the inverse ƒ^–1 maps 3 back to a. In mathematics, if ƒ is a function from a set A to a set B, then an inverse function for ƒ is a function from B to A, with the property that a round trip from A to B to A (or from B to A to B) returns each element of the initial set to itself.

Simplify : 12 – ( x + 3 ) +10

Solution:

You can simply 12 – ( x + 3 ) +10 by rearranging the terms:

1. 12 –x -3 +10
2. 19-x

I need to know how to do problems like this, I Want to know how to solve, and simplify them, and also finding slopes. Like these kinds of problems (Write the equation, 3x + 5y = 15, in the slope intercept form (y = mx + b))

Here’s how you solve this type of question:

1. Start with an equation like 3x + 5y = 15
2. Move 3x to the other side, so 5y = 15 – 3x
3. Divide both sides by 5, so y = 3 – x
4. Another way of writing this is y = -.6x + 3, or y=mx = b, where m=-0.6 and b = 3
5. If m = -0.6, that means that the slope =-0.6



Determine the next two values in the following pattern of numbers: 1, 4, 9, 61, 52, 63, 94, ___, ___ .

Solution:

This is a well known “trick question”. It’s simply a series of squares with the digits reversed:

1² = 1   => 1

2² = 4   => 4

3² = 9   => 9

4² = 16 => 61

5² = 25 => 52

6² = 36 => 63

7² = 49 => 94

8² = 64 => 46

9² = 81 => 18

How do you find the area of a base on a 3-D rectangle?

Here’s how you solve this type of question:

1. The base of the 3D rectangle is in the shape of a 2D rectangle.
2. Multiply the length of this 2D rectangle by its width to let the area

What is mean?

Solution:

The arithmetic mean is the average.

http://en.wikipedia.org/wiki/Arithmetic_mean

A close rectangular box measuring 72cm by 54cm by 48cm externally is made up of wood find the capacity of the box in litres,the volume of woodused in making the box,and the mass of the box if the density of the wood used is 0.9g/cmcube

Solution:

Volume of wood is 72*54*48 = 186,624 cmcube; the mass would be 186,624 * 0.9 = 167,961.6 g.

A father is 3 times older than his son and the sum of their ages is 40 years. Find their present age?

Solution:

If we let the age of the father be “F”, and the age of the son be “S”, then we know the following:

1. F = 3 x S
2. F+S=40

Therefore, F=3x(40-F)…so 4F=120.

Therefore, F=30 and S=10.