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.

Solution:

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

1. 12 –x -3 +10
2. 19-x

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



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

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

Solution:

The arithmetic mean is the average.

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

Solution:

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

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.