Which of the following is true
If number of elements in set $A$ are finite, such that $f : A \to A$ is an one-one function, then $f$ is necessarily onto
If a function is continuous in its domain and changes its sign for any $2$ values of $x$ then odd number of roots lie between the given values of $x$
If $f : A \to A$ is one-one then it must be onto
It is possible that a curve contains a local maxima and a global minima at the same point
Consider a function $f : N \rightarrow R$, satisfying $f(1)+2 f(2)+3 f(3)+\ldots+x f(x)=x(x+1) f(x) ; x \geq 2$ with $f(1)=1$. Then $\frac{1}{f(2022)}+\frac{1}{f(2028)}$ is equal to
Domain of $f (x)$ = $\sqrt {{{\log }_2}\left( {\frac{{10x - 4}}{{4 - {x^2}}}} \right) - 1} $ , is
If function $f(x) = \frac{1}{2} - \tan \left( {\frac{{\pi x}}{2}} \right)$; $( - 1 < x < 1)$ and $g(x) = \sqrt {3 + 4x - 4{x^2}} $, then the domain of $gof$ is
If for the function $f(x) = \frac{1}{4}{x^2} + bx + 10$ ; $f\left( {12 - x} \right) = f\left( x \right)\,\forall \,x\, \in \,R$ , then the value of $'b'$ is
Let $\mathrm{f}: \mathrm{R} \rightarrow \mathrm{R}$ be a function which satisfies $\mathrm{f}(\mathrm{x}+\mathrm{y})=\mathrm{f}(\mathrm{x})+\mathrm{f}(\mathrm{y}) \forall \mathrm{x}, \mathrm{y} \in \mathrm{R} .$ If $\mathrm{f}(1)=2$ and $g(n)=\sum \limits_{k=1}^{(n-1)} f(k), n \in N$ then the value of $n,$ for which $\mathrm{g}(\mathrm{n})=20,$ is