Functions

The number of distinct real roots of the equation $|x||x+2|-5|x+1|-1=0$ is_______

If the function $f:(-∞, -1]\rightarrow (a, b)]$ defined by $f(x)={e}^{{x}^{3}-3x+1}$ is one-one and onto, then the distance of the point $P(2b+4, a+2)$ from the line $x+{e}^{-3}y=4$ is:

Let $A=$ { $x\in\,R:x$ is not a positive integer} $.$ Define a function $f:A\rightarrow\,R$ as $f\left(x\right)=\frac{2x}{x-1}$ , then $f$ is:

Let$f:R\rightarrow\,R$and$g:R\rightarrow\,R$be defined as$f\left(x\right)=\left{\begin{matrix} \log\,_{e}x, & x>0 \\ e^{-x}, & x\leq\,0 \end{matrix}\right$and$g\left(x\right)=\left{\begin{matrix} x, & x\geq\,0 \\ e^{x},…

Let $f:R-\left{2,6\right}\rightarrow\,R$ be real valued function defined as $f\left(x\right)=\frac{x+2x+1}{x^{2}-8x+12}$. Then range of $f$ is

The number of bijective function $f\left(1,3,5,7,\cdots\,,99\right)\rightarrow\,\left(2,4,6,8,\cdots\,,100\right)$ if $f\left(3\right)>f\left(5\right)>f\left(7\right)\cdots\,>f\left(99\right)$ is

Let $R={a,b,c,d,e}$and $S={1,2,3,4}$. Total number of onto functions $f:R\rightarrow\,S$ such that $f(a)\neq\,1$, is equal to ________.

Let $f\left(x\right)=2^{x}-x^{2},x\in\,R$. If $m$ and $n$ are respectively the number of points at which the curves $y=f\left(x\right)$ and $y=f^{'}\left(x\right)$ intersects the $x-$axis, then the value of$m+n$ is

Consider the function $f:\left[\frac{1}{2},1\right]\rightarrow\,R$ defined by $f\left(x\right)=4\sqrt{2}x^{3}-3\sqrt{2}x-1$. Consider the statements (I) The curve $y=f\left(x\right)$ intersects the $x$-axis exactly at…

If the domain of the function $f\left(x\right)=\frac{\left[x\right]}{1+x^{2}}$, where $\left[x\right]$ is greatest integer $\leq\,x$, is $[2,6)$, then its range is

Let $f:R\rightarrow\,R$ be a function such that $f\left(x\right)=\frac{x^{2}+2x+1}{x^{2}+1}$. Then

The number of elements in the set$\left{x\in\,R:\left(|x|-3\right)\left|x+4\right|=6\right}$ is equal to