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Home » Let f : N → N be defined by and State whether the function f is bijective. Justify your answer
Let f : N → N be defined by and State whether the function f is bijective. Justify your answer
CBSE | Class 12 | Maths | NCERT | Relations and Functions
Let f : N → N be defined by and State whether the function f is bijective. Justify your answer

Arrangement:

For n = 1, 2

f(1) = (n+1)/2 = (1+1)/2 = 1 and f(2) = (n)/2 = (2)/2 = 1

f(1) = f(2), yet 1 ≠ 2

f isn’t one-one.

For a characteristic number, “a” in co-space N

In case n is odd

n = 2k + 1 for k ∈ N , then, at that point 4k + 1 ∈ N to such an extent that f(4k+1) = (4k+1+1)/2 = 2k + 1

In case n is even

n= 2k for some k ∈ N to such an extent that f(4k) = 4k/2 = 2k

f is onto

In this manner, f is onto however not bijective capacity.

Solution:

For n = 1, 2

f(1) = (n+1)/2 = (1+1)/2 = 1 and f(2) = (n)/2 = (2)/2 = 1

f(1) = f(2), yet 1 ≠ 2

f isn’t one-one.

For a characteristic number, “a” in co-space N

In case n is odd

n = 2k + 1 for k ∈ N , then, at that point 4k + 1 ∈ N to such an extent that f(4k+1) = (4k+1+1)/2 = 2k + 1

In case n is even

n= 2k for some k ∈ N to such an extent that f(4k) = 4k/2 = 2k

f is onto

In this manner, f is onto however not bijective capacity.

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