Embibe Experts Solutions for Exercise 9: Assignment

If $f\left(x\right)=\left|\left[x\right]\right|$ and $g\left(x\right)=\left[\left|x\right|\right]$, where $\left[·\right]$ represents greatest integer function, then which of the following is correct?

The interval(s) of the value of $x$ for which $\left|x-3\right|+\left|2x-3\right|=3\left|x-2\right|$ is/are

Let $A$ be the domain of the function $f\left(x\right)=\frac{3}{\sqrt{9-x^2}}+{\log }_{\left|x-3\right|}\left(x+3\right)$. Then the subset(s) of $A$ is/are

If $n\left(f_1\left(x\right),f_2\left(x\right)\right)$ denotes the number of solutions of the equation $f_1\left(x\right)=f_2\left(x\right)$, then which of the following is/are CORRECT?

The equation $\left|\left|x\right|-3\right|+\left|x+3\right|=\lambda$ has

Let a function $f$ defined on the set of all integers satisfying $f\left(0\right)\ne 0, f\left(1\right)=5$ and $f\left(x\right)·f\left(y\right)=f\left(x+y\right)+f\left(x-y\right)$ for all integers $x$ and $y$. Then

If $f\left(x\right)=\left|5-\left|x\right|\right|$ and $g\left(x\right)=7^{-\left|x\right|}$ then

Let two curves are $\left|y\right|=\left(x-1\right)\left(x-3\right)$ and $\left|y+1\right|=2x+3$, then number of point(s) of intersection of these two curves in