Functions

$f(x)=\log \left(\left(\frac{2 x^2-3}{x}\right)+\sqrt{\frac{4 x^4-11 x^2+9}{|x|}}\right)$ is

The range of the function $f(x)=\frac{x}{x^2-5 x+9}$ is

Match the following

The velocity of a particle which starts from rest is given by the following table. The total distance travelled (in metre) by the particles in $10 \mathrm{~s}$, using Trapezoidal rule is given by

Let $R$ denote the set of all real numbers and $R^{+}$denote the set of all positive real numbers. For the subsets $A$ and $B$ of $R$ define $f: A \rightarrow B$ by $f(x)=x^2$ for $x \in A$. Observe the two lists given…

The function $f: C \rightarrow C$ defined by $f(x)=\frac{a x+d}{c x+d}$ for $x \in C$ where $b d \neq 0$ reduces to a constant function, if

The domain of the function $f(x)=\sqrt{\frac{4-x^2}{[x]+2}}$, where $[x]$ denotes the greatest integer not more than $x$, is

If $A \subseteq Z$ and the function $\mathrm{f}: \mathrm{A} \rightarrow \mathrm{R}$ is defined by $f(x)=\frac{1}{\sqrt{64-(0.5)^{24+x-x^2}}}$ then the sum of all absolute values of elements of A is

The domain of defined of the function $f(x)=\sqrt{\frac{1-|x|}{2-|x|}}$ is

Let $[\mathrm{x}]$ represent the greatest integer less than or equal to $\mathrm{x},\{\mathrm{x}\}=\mathrm{x}-[\mathrm{x}]$, $\sqrt{2}=1.414$ and $\sqrt{3}=1.732$. If $f(x)=\left\{x+\left[\frac{x}{1+x^2}\right]\right\}$…

The set of all real values of $x$ such that $f(x)=\sqrt{\frac{[x]-1}{[x]^2-[x]-6}}$ is a real valued function is

If $f: R \rightarrow R$ and $g: R \rightarrow R$ are two functions defined by $f(x)=2 x-3$ and $g(x)=5 x^2-2$, then the least value of the function $(g \circ f)(x)$ is