Question #307094

Discussion Assignment



Let f(x)=\sqrt(x) with f: \mathbb{R} \to \mathbb{R}. Discuss the properties of f. Is it injective, surjective, bijective, is it a function? Why or why not? Under what conditions change this?





Explain using examples.

1
Expert's answer
2022-03-08T03:43:03-0500

1) take x=-1, the function is not defined on it.

2) the function does not take the value -1

It follows that the function is not bijective, surjective, injective.

to change this, you need to change the scope and scope

if f: [0,+\infin )->[0,+\infin ) then function is bijective, surjective, injective.

if f:R->[0,+\infin ) then function is only surjective

if f: [0,+\infin )->R then function is only injective



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