Functions

Consider the following statements in respect of the function $f(x)=\left\{\begin{array}{cc} |x|+1, & 0 \lt |x| \leq 3 \\ 1, & x=0 \end{array}\right.$ The function attains maximum value only at $x=3$ The function attains…

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

A function is defined by $f(x)=\pi+\sin ^2 x$ What is the range of the function?

Let $f(x)$ and $g(x)$ be two functions such that $g(x)=x-\frac{1}{x}$ and $f$ o $g(x)=x^3-\frac{1}{x^3}$. What is $g[f(x)-3 x]$ equal to?

A function satisfies $f(x-y)=\frac{f(x)}{f(y)}$, where $f(y) \neq 0$. If $f(1)=0.5$, then what is $f(2)+f(3)+f(4)+f(5)+f(6)$ equal to?

Paragraph: Let $f(x)=[x]^2-\left[x^2\right]$. Question: What is $f(0.999)+f(1.001)$ equal to?

Consider the following statements in respect of the function $f(x)=x$ in the interval $(-1,1)$ : I. The function attains maximum value. II. The function attains minimum value. Which of the statements given above is/are…

What is the domain of the function $f(x)=\sqrt{1-(x-1)^2}$ ?

Paragraph: Consider the function $f(x)=|x-2|+|3-x|+|4-x|$, where $x \in R$ Question: At what value of $x$ does the function attain minimum value?

Let $f(x) f(y)=f(x y)$ for all real $x, y$. If $f(2)=4$, then what is the value of $f\left(\frac{1}{2}\right)$ ?

If $f(x)=a x-b$ and $g(x)=c x+d$ are such that $f(g(x))=g(f(x))$, then which one of the following holds?

Let $f(x)=x^2-1$ and $\operatorname{gof}(x)=x-\sqrt{x}+1$ Which one of the following is a possible expression for g(x)?