Which of the following statements are true, and which are false?

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

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