$\frac{1}{x + 1} + x - 1 = \frac{1}{x^{2}}$
Given that, which of the following is the expression $x^{3} - 1$ equal to?
A) $\frac{2}{x - 1}$ B) $\frac{1}{x}$ C) $\frac{x - 1}{x}$ D) $-x$ E) $\frac{1}{x + 1}$

A function f defined on the set of natural numbers is defined for every n as
$$f ( n ) = \begin{cases} 5 n + 40 , & 0 \leq n < 10 \\ f ( n - 10 ) , & n \geq 10 \end{cases}$$
Example: $f ( 23 ) = f ( 13 ) = f ( 3 ) = 5 \cdot 3 + 40 = 55$
Accordingly, what is the sum of the two-digit numbers AB that satisfy the equation $f ( A B ) = A B$?
A) 75 B) 80 C) 90 D) 100 E) 105

$$f ( x ) = \left\{ \begin{array} { l l l } 10 - x ^ { 2 } & , & x < 0 \\ a x + b & , & 0 \leq x \leq 3 \\ ( 1 - x ) ^ { 2 } & , & x > 3 \end{array} \right.$$
The function is continuous on the set of real numbers.
Accordingly, what is the sum $\mathbf { a } + \mathbf { b }$?
A) 16 B) 15 C) 12 D) 9 E) 8

Let a be a real number. A function f is defined on the set of real numbers as
$$f ( x ) = \left\{ \begin{array} { c c c } a - x & , & x < 1 \\ 5 x - 4 & , & 1 \leq x \leq 5 \\ ( x - a ) ^ { 2 } + 12 & , & x > 5 \end{array} \right.$$
If there is only one point where the function f is not continuous, what is the value of
$$f ( 7 ) - f ( 0 )$$?
A) 3
B) 4
C) 5
D) 6
E) 7