F-N- N- 1-2-3 defined by fx-x-3 is

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Standard XII

Mathematics

Inverse of a Function

f:N→ N- 1,2,3...

Question

$f : N \to N - {1, 2, 3}$ defined by $f (x) = x + 3$ is

one-one only

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onto only

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bijective

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neither one-one nor onto

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Solution

The correct option is C bijective
$f (x) = x + 3$
$f (x)$ is monotonically increasing function.
So $f (x)$ is one - one.
Also $f (x)$ takes the value of all natural numbers except ${1, 2, 3}$ in its domain.
Here range $=$ codomain
So $f (x)$ is onto also.
Thence, it is bijective.

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f:N→N−{1,2,3} defined by f(x)=x+3 is

The correct option is C bijectivef(x)=x+3f(x) is monotonically increasing function.So f(x) is one - one.Also f(x) takes the value of all natural numbers except {1,2,3} in its domain.Here range = codomainSo f(x) is onto also.Thence, it is bijective.

$f : N \to N - {1, 2, 3}$ defined by $f (x) = x + 3$ is

The correct option is C bijective
$f (x) = x + 3$
$f (x)$ is monotonically increasing function.
So $f (x)$ is one - one.
Also $f (x)$ takes the value of all natural numbers except ${1, 2, 3}$ in its domain.
Here range $=$ codomain
So $f (x)$ is onto also.
Thence, it is bijective.