Calculus/Precalculus/Exercises

Which one of the following is a true statement?
Hint: the true statement is often referred to as the triangle inequality. Give examples where the other two are false.

Functions
52. Let $$f(x)=x^2$$.

53. Let $$f(x)=x+2$$, $$g(x)=1/x$$.
 * a. Give formulae for

55. Consider the following function
 * $$f(x)=\begin{cases}-\frac{1}{9} & \mbox{if }x<-1 \\2 & \mbox{if }-1\le x\le 0 \\x+3 & \mbox{if }x>0 \end{cases}$$

56. Consider the following function
 * $$f(x)=\begin{cases}x^2 & \mbox{if }x>0 \\-1 & \mbox{if }x\le 0 \end{cases}$$

57. Consider the following function
 * $$f(x)=\frac{\sqrt{2x-3}}{x-10}$$

58. Consider the following function
 * $$f(x)=\frac{x-7}{x^2-49}$$