Special Functions

For any real number x, the maximum value of $4–6x–x^2$ is ?

The decision between shifting and reducing is done through a relation $\mathrm{P} \mathrm{C} (\mathrm{V} \mathrm{U} \{\$\} * (? \mathrm{U} \{\$\})$, called a _____ where V is an alphabet; $?$ is set of terminals, S is the start symbol.

If $x$ is a negative real number, then

The general value of  $\theta$ satisfying the equation  ${2\sin }^2\theta -3\sin \theta -2=0$ , is

Consider the function $f\left(x\right)=\left|x-2\right|+\left|3-x\right|+\left|4-x\right|$

At what value of $x$ does the function attain minimum value?

Let $f\left(x\right)=\sin \left[{\pi }^2\right]x+\cos \left[-{\pi }^2\right]x$ where $\left[.\right]$ is a greatest integer function

What is $f\left(\frac{\pi }{4}\right)$ equal to?

Let $f\left(x\right)=\sin \left[{\pi }^2\right]x+\cos \left[-{\pi }^2\right]x$ where $\left[.\right]$ is a greatest integer function

What is $f\left(\frac{\pi }{2}\right)$ equal to?

What is the range of the function $f\left(x\right)=x+\left|x\right|$ if the domain is the set of real numbers?

The number of integral solution $x$ of ${\log }_{\left(x+\frac{7}{2}\right)}{\left(\frac{x-7}{2x-3}\right)}^2\ge 0$ is

Let $a, b, c$ be the three distinct positive real numbers such that ${\left(2a\right)}^{{\log }_{e}a}={\left(bc\right)}^{{\log }_{e}b}$ and $b^{{\log }_{e}2}=a^{{\log }_{e}c}$ Then $6a+5bc$ is equal to ______.

What is logarithmic function?

Area ( in sq. units) included between $y=f\left(x\right)=\left|x-1\right|+\left|x-2\right|$ and $y=3$ is

Solution of inequality

${\log }_{\sin x}\left({\log }_3\left({\log }_{0.2}\left(x\right)\right)\right)<0$ is

Prove that the greatest integer function defined by $f\left(x\right)=\left[x\right]; 0<x<3$ is not differentiable at $x=1$ and $x=2$.

Find the number of solutions of $\left|x\right|3^{\left|x\right|}=1$.

Solution set of the inequality $\left|6-x\right|+3<2$ is

Let $\alpha , \beta$ and $\gamma$ be the real solutions of $2e^{-\left\{x\right\}}=x+1$, then (where, $\left\{·\right\}$ is the fractional part function)

The graph shows in figure is exponential. Write down the equation corresponding to the graph.