[SOLVED] Simple Functions

I've got a few questions regarding Functions which are bothering me.

Q1: Find the largest possible domain of each of the following functions:

**a)** $\displaystyle 1/x-2$

**Answer =** All real numbers except 2

Why is this? Also why can't we use negative integers for x e.g -2

**b)** $\displaystyle 1/(x-1)(x-2)$

**Answer =** All real numbers except 1 and 2

Why is this? Also why can't we use negative integers for x e.g -2 (i guess it's same as the part (a) I posted)

Q2: The domains of these functions are the set of all positive real numbers. Find their ranges:

**a)** $\displaystyle f(x) = (x-1)^2 + 2$

Generally I'd put the least real number value (0) into the function and get the least range. In this case my answer is not matching with the real answer.

**Answer =** f(x) is greater than or equal to 2

**Q3: Find the range of each if the following functions. All the functions are defined for all real values of x:**

a) $\displaystyle f(x) = 3(x+5)^2+2$

Answer = f(x) is greater than or equal to 2How is that?

b) $\displaystyle f(x) = 2(x+2)^4-1$

**Answer =** f(x) is greater than or equal to -1

How is that?

Thanks in advance!