Functions

Consider the curves $\mathrm{y}=|\mathrm{x}-1|$ and $|\mathrm{x}|=2$ What is/are the point(s) of intersection of the curves?

Which one of the following is correct in respect of the graph of $y=\frac{1}{x-1}$ ?

For each non-zero real number x , let $f(x)=\frac{x}{|x|}$. The range of $f$ is

Let $\mathrm{A}=\{x \in \mathrm{R}:-1 \lt x \lt 1\}$. Which of the following is/are bijective functions from A to itself? $f(x)=x|x|$ $g(x)=\cos (\pi x)$ Select the correct answer using the code given below:

Consider the following in respect of the function $f(x)=10^x$ : Its domain is $(-\infty, \infty)$ It is a continuous function It is differentiable at $x=0$ Which of the above statements are correct?

Afunction $f: A \rightarrow R$ is defined by the equation $f(x)=x^2-4 x+5$ where $A=(1,4)$. What is the range of the function?

Let $f$ be a function from the set of natural numbers to the set of even natural numbers given by $f(x)=2 x$. Then $f$ is

Consider the following statements in respect of the function $y=[x], x \in(-1,1)$ where [.] is the greatest integer function: Its derivative is 0 at $x=0.5$ It is continuous at $x=0$ Which of the above statements is/are…

The minimum value of the function $f(x)=|x-4|$ exists at

Consider the curves $f(x)=x|x|-1$ and $g(x)= \begin{cases}\frac{3 x}{2}, & x \gt 0 \\ 2 x, & x \leq 0\end{cases}$ Where do the curves intersect?

Consider the function $\mathrm{f}(\mathrm{x})=\frac{27\left(\mathrm{x}^{2 / 3}-\mathrm{x}\right)}{4}$ How many solutions does the function $\mathrm{f}(\mathrm{x})=1$ have?

The function $f: \mathrm{X} \rightarrow \mathrm{Y}$ defined by $f(\mathrm{x})=\cos \mathrm{x}$, where $\mathrm{x} \in \mathrm{X}$, is one-one and onto if X and Y are respectively equal to