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iren [92.7K]
3 years ago
10

Suppose f is the function f(x) = |x - 5| + 5 and f : Z -> Z

Mathematics
1 answer:
svp [43]3 years ago
7 0

Answer:

No, function is not one-to-one

No, function is not onto

Step-by-step explanation:

We are  given that a function

f:Z\rightarrow Z

f(x)=\mid{x-5}\mid +5

If function is one-to-one then different x have different image .

Domain =Z

Codomain=Z

When function is onto then range=Codomain

Substitute x=1

Then ,f(1)=\mid{1-5}\mid+5=4+5=9

When substitute x=9

Then , we get f(9)=\mid {9-5}\mid +5=4+5=9

Image of 1  and 9 are same hence, function is not one-to-one.

Negative elements of Z and Zero  has no preimage.Therefore, function is not onto.

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