The number of functions $f$, from the set$A=\left\{x \in N: x^{2}-10 x+9 \leq 0\right\}$ to the set $B=\left\{n^{2}: n \in N\right\}$ such that $f(x) \leq(x-3)^{2}+1$, for every $x \in A$, is.
$1440$
$1450$
$1460$
$1470$
Show that the function $f: N \rightarrow N$ given by $f(x)=2 x,$ is one-one but not onto.
If $f(x) = \log \left[ {\frac{{1 + x}}{{1 - x}}} \right]$, then $f\left[ {\frac{{2x}}{{1 + {x^2}}}} \right]$ is equal to
Let, $f(x)=\left\{\begin{array}{l} x \sin \left(\frac{1}{x}\right) \text { when } x \neq 0 \\ 1 \text { when } x=0 \end{array}\right\}$ and $A=\{x \in R: f(x)=1\} .$ Then, $A$ has
Let $A=\{1,2,3,4,5\}$ and $B=\{1,2,3,4,5,6\}$. Then the number of functions $f: A \rightarrow B$ satisfying $f(1)+f(2)=f(4)-1$ is equal to
Show that the Modulus Function $f : R \rightarrow R$ given by $(x)=|x|$, is neither one - one nor onto, where $|x|$ is $x$, if $x$ is positive or $0$ and $| X |$ is $- x$, if $x$ is negative.