Let f : R→R be given by


Let $f: R \rightarrow R$ be given by $f(x)=\left[x^{2}\right]+[x+1]-3$ where $[x]$ denotes the greatest integer less than or equal to $x$. Then, $f(x)$ is

(a) many-one and onto

(b) many-one and into
(c) one-one and into
(d) one-one and onto


(b) many-one and into

$f: R \rightarrow R$


It is many one function because in this case for two different values of x
we would get the same value of f(x) .


$x=1.1,1.2 \in R$









It is into function because for the given domain we would only get the integral values of
but R is the codomain of the given function.
That means , CodomainRange
Hence, the given function is into function.
Therefore, f(x) is many one and into


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