f(x) Transforms to f(|x|)

Q. The number of solution(s) of $y=||x{|}^2-2|x|-2|$ and $y=1$ is

1. $2$
2. $3$
3. $4$
4. $5$

Q. The graph of $f\left(x\right)=||x-1|-1|$ is

1. 
2. 
3. 
4. 

Q. Plot the graph of ${\cos }^{-1}x$ and write its domain and range.

Q. The graph of $f\left(x\right)=||x-1|-1|$ is

1. 
2. 
3. 
4. 

Q. Match the following by appropriately matching the lists based on the information given in Column $1$ and Column $2$
$\begin{array}{cc}Column1:& Column2:\\ \text{Equation}& \text{Number}\\ & \text{of roots}\\ \text{a.}{x}^2\tan x=1,x\in [0,2\pi ]& \text{p.}5\\ \text{b.}{2}^{\cos x}=|\sin x|,x\in [0,2\pi ]& \text{q.}2\\ \text{c.}\text{If}f\left(x\right)\text{is a polynomial of degree}& \\ 5\text{with real coefficients such that}& \\ f\left(|x|\right)=0\text{has}8\text{real roots, then the}& \\ \text{number of roots of}f\left(x\right)=0\text{is/are}& \text{r.}3\\ \text{d.}{7}^{|x|}(|5-|x||)=1& \text{s.}4\end{array}$

Then which of the following is correct ?

1. $a\to s,b\to r,c\to p,d\to q$
2. $a\to q,b\to s,c\to p,d\to s$
3. $a\to q,b\to s,c\to p,d\to r$
4. $a\to p,b\to r,c\to q,d\to s$

Q. The graph of the hyperbolic cosine function for all real values is:

1. Strictly increasing
2. Strictly decreasing
3. Strictly increasing in the interval $[0,\infty )$ and Strictly decreasing in the interval $(-\infty ,0]$
4. Strictly increasing in the interval $(-\infty ,0]$ and Strictly decreasing in the interval $[0,\infty )$

Q. The graph of $f\left(x\right)=x^2-3|x|+2$ is

1. 
2. 
3. 
4. 

Q. Match the following by appropriately matching the lists based on the information given in Column $1$ and Column $2$
$\begin{array}{cc}Column1:& Column2:\\ \text{Equation}& \text{Number}\\ & \text{of roots}\\ \text{a.}{x}^2\tan x=1,x\in [0,2\pi ]& \text{p.}5\\ \text{b.}{2}^{\cos x}=|\sin x|,x\in [0,2\pi ]& \text{q.}2\\ \text{c.}\text{If}f\left(x\right)\text{is a polynomial of degree}& \\ 5\text{with real coefficients such that}& \\ f\left(|x|\right)=0\text{has}8\text{real roots, then the}& \\ \text{number of roots of}f\left(x\right)=0\text{is/are}& \text{r.}3\\ \text{d.}{7}^{|x|}(|5-|x||)=1& \text{s.}4\end{array}$

Then which of the following is correct ?

1. $a\to s,b\to r,c\to p,d\to q$
2. $a\to q,b\to s,c\to p,d\to s$
3. $a\to q,b\to s,c\to p,d\to r$
4. $a\to p,b\to r,c\to q,d\to s$

Q. Plot the point $(x,y)$ given in the following table in the graph.x

x	-3	6	-4
y	5	-4	-3

Q. The number of solution(s) of $|x^3-1|=x$ is

Q. The graph a function $f$ is given. State the domain and range of $f$

1. $[-2,3]$, $[-3,3]$
2. $[-3,2]$, $[-2,3]$
3. $[-3,3]$, $[-2,3]$
4. none of these

Q. The graph of $f\left(x\right)=||x-1|-1|$ is

1. 
2. 
3. 
4. 

Q. The number of solution(s) of $y=||x{|}^2-2|x|-2|$ and $y=1$ is

1. $2$
2. $3$
3. $4$
4. $5$

Q. The number of solution(s) of $y=||x{|}^2-2|x|-2|$ and $y=1$ is

1. $2$
2. $3$
3. $4$
4. $5$

Q. Which of the following is/are true for $f\left(x\right)=\frac{4x+3}{x^2+1}$

1. Total number of real root of equation $f\left(x\right)=0$ is $1$
2. Range of $f\left(x\right)$ is $[-1,4]$
3. Equation $f\left(x\right)=2$ will have two real and distinct roots
4. Total number of real roots of equation $f\left(x\right)=0$ are $3$

Q. Select the correct graph of the function $f\left(x\right)=\tan |x+\frac{\pi }{3}|.$

1. 
2. 
3. 

Q. The graph of $f\left(x\right)=x^2-3|x|+2$ is

1. 
2. 
3. 
4.