Calculus/Precalculus/Exercises

Algebra

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. Template:Question-answer Template:Question-answer Template:Question-answer

Functions

52. Let $f(x)=x^2$ . Template:Question-answer Template:Question-answer Template:Question-answer

53. Let $f(x)=x+2$ , $g(x)=1/x$ .

a. Give formulae for

55. Consider the following function

$f(x)=\{\begin{array}{cc}-\frac{1}{9}& \text{if }x<-1\\ 2& \text{if }-1\le x\le 0\\ x+3& \text{if }x>0\end{array}$

56. Consider the following function

$f(x)=\{\begin{array}{cc}{x}^2& \text{if }x>0\\ -1& \text{if }x\le 0\end{array}$

57. Consider the following function

$f(x)=\frac{\sqrt{2x-3}}{x-10}$

58. Consider the following function

$f(x)=\frac{x-7}{x^2-49}$