The function f: N N is defined by f(n)= ll n+1 2 , & if n is odd … - Vidyadip

MCQ

The function $f: N \rightarrow N$ is defined by $f(n)=\left\{\begin{array}{ll}\frac{n+1}{2}, & \text { if } n \text { is odd } \\ \frac{n}{2}, & \text { if } n \text { is even }\end{array}\right.$
The function $f$ is

A
bijective
B
one-one but not onto
C
onto but not one-one
D
neither one-one nor onto

✓

Answer

Given, $f(x)=\left\{\begin{array}{cl}\frac{n+1}{2}, & \text { if } n \text { is odd } \\ \frac{n}{2}, & \text { if } n \text { is even }\end{array}\right.$
Now, $f(1)=\frac{1+1}{2}=1, f(2)=\frac{2}{2}=1$
$\Rightarrow f(1)=f(2)$ but $1 \neq 2 \therefore f$ is not one-one.
But $f$ is onto $(\because$ range of $f$ is $N$.)

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