Which of the following statements are true, and which are false? Give reasons for your answers in the form of a short proof or a counter example.

i) There are at least two ways of describing the set ,8,7{ . …}

ii) Any function with domain R×R is a binary operation.

iii) The graph of every function from ]1,0[ to R is infinite.

iv) The function :f R → R , defined by )x(f = x x , is an odd function.

v) The domain of the function ,g f o where )x(f = x and )x(g = 2 − ,x is ]2, ]−

Answer:

i) There are at least two ways of describing the set ,8,7{ . …}

**True**

ii) Any function with domain R×R is a binary operation.

**True**

iii) The graph of every function from ]1,0[ to R is infinite.

**False**

iv) The function :f R → R , defined by )x(f = x x , is an odd function.

**True**

v) The domain of the function ,g f o where )x(f = x and )x(g = 2 − ,x is ]2, ]−

**True**