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
If $y = 3[x] + 1 = 4[x -1] -10$, then $[x + 2y]$ is equal to (where $[.]$ is $G.I.F.$)
If domain of the function $\log _e\left(\frac{6 x^2+5 x+1}{2 x-1}\right)+\cos ^{-1}\left(\frac{2 x^2-3 x+4}{3 x-5}\right)$ is $(\alpha, \beta) \cup(\gamma, \delta]$, then $18\left(\alpha^2+\beta^2+\gamma^2+\delta^2\right)$ is equal to $....$.
The domain of $f(x) = [\sin x] \cos \left( {\frac{\pi }{{[x - 1]}}} \right)$ is (where $[.]$ denotes $G.I.F.$)
The graph of function $f$ contains the point $P (1, 2)$ and $Q(s, r)$. The equation of the secant line through $P$ and $Q$ is $y = \left( {\frac{{{s^2} + 2s - 3}}{{s - 1}}} \right)$ $x - 1 - s$. The value of $f ‘ (1)$, is
Consider the function $\mathrm{f}:\left[\frac{1}{2}, 1\right] \rightarrow \mathrm{R}$ defined by $f(x)=4 \sqrt{2} x^3-3 \sqrt{2} x-1$. Consider the statements
$(I)$ The curve $y=f(x)$ intersects the $x$-axis exactly at one point
$(II)$ The curve $y=f(x)$ intersects the $x$-axis at $\mathrm{x}=\cos \frac{\pi}{12}$
Then