Question #305791

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
2022-03-07T08:13:02-0500

f(x)=12x>0, for x[0,+)f'(x)=\frac{1}{2\sqrt{x}}>0, \ for\ x\in[0,+\infin)


f is not surjective and injective since the range and domain are [0,+\infin )

for f to be a bijection is necessary and sufficient, f must be injection and surjection=>

f is not bijective

if f:[0,+\infin )->[0,+\infin )

f-increasing function сonsequently exist 

f1f^{-1}

f- is bijective=>f is injective and surjective


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