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Recent questions tagged functions

0 votes
1 answer
1
If $f:\{a,b\}^{\ast}\rightarrow \{a,b\}^{\ast }$ be given by $f(n)=ax$ for every value of $n\in \{a,b\}$, then $f$ is one to one not onto one to one and onto not one to one and not onto not one to one and onto
asked Apr 2, 2020 in Set Theory & Algebra Lakshman Patel RJIT 173 views
1 vote
1 answer
2
1 vote
1 answer
4
0 votes
1 answer
6
The functions mapping $R$ into $R$ are defined as : $f\left(x \right)=x^{3} - 4x, g\left(x \right)=\frac{1}{x^{2}+1}$ and $h\left(x \right)=x^{4}.$ Then find the value of the following composite functions : $h_{o}g\left(x \right)$ and $h_{o}g_{o}f\left(x \right)$ ... $\left ( x^{2}+1 \right )^{-4}$ and $\left [ \left ( x^{3}-4x \right )^{2}+1 \right ]^{-4}$
asked Mar 24, 2020 in Set Theory & Algebra jothee 127 views
0 votes
2 answers
7
Which of the following cannot be passed to a function in C++? Constant Structure Array Header file
asked Mar 24, 2020 in Object Oriented Programming jothee 347 views
0 votes
1 answer
8
Which one of the following is correct for overloaded functions in $C++$? Compiler sets up a separate function for every definition of function. Compiler does not set up a separate function for every definition of function. Overloaded functions cannot handle different types of objects. Overloaded functions cannot have same number of arguments.
asked Mar 24, 2020 in Object Oriented Programming jothee 205 views
1 vote
1 answer
9
X AND Y is an arbitrary sets, F: $X\rightarrow Y$ show that a and b are equivalent F is one-one For all set Z and function g1: $Z\rightarrow X$ and g2: $Z\rightarrow X$, if $g1 \neq g2$ implies $f \bigcirc g1 \neq f \bigcirc g2$ Where $\bigcirc$ is a fucntion composition.
asked Feb 17, 2020 in Set Theory & Algebra vivek_mishra 310 views
3 votes
1 answer
10
In the following procedure Integer procedure P(X,Y); Integer X,Y; value x; begin K=5; L=8; P=x+y; end $X$ is called by value and $Y$ is called by name. If the procedure were invoked by the following program fragment K=0; L=0; Z=P(K,L); then the value of $Z$ will be set equal to $5$ $8$ $13$ $0$
asked Jan 13, 2020 in Programming Satbir 696 views
2 votes
2 answers
11
If $f(x)$ is a real valued function such that $2f(x)+3f(-x)=15-4x$, for every $x \in \mathbb{R}$, then $f(2)$ is $-15$ $22$ $11$ $0$
asked Sep 23, 2019 in Calculus Arjun 203 views
2 votes
3 answers
12
If $f(x) = \dfrac{\sqrt{3} \sin x}{2+\cos x}$, then the range of $f(x)$ is the interval $[-1 , \sqrt{3}{/2}]$ the interval $[-\sqrt{3}{/2}, 1]$ the interval $[-1, 1]$ none of these
asked Sep 23, 2019 in Calculus Arjun 148 views
1 vote
0 answers
13
Suppose that the function $h(x)$ is defined as $h(x)=g(f(x))$ where $g(x)$ is monotone increasing, $f(x)$ is concave, and $g’’(x)$ and $f’’(x)$ exist for all $x$. Then $h(x)$ is always concave always convex not necessarily concave None of these
asked Sep 23, 2019 in Calculus Arjun 143 views
0 votes
1 answer
14
Let $f(x) = \dfrac{2x}{x-1}, \: x \neq 1$. State which of the following statements is true. For all real $y$, there exists $x$ such that $f(x)=y$ For all real $y \neq 1$, there exists $x$ such that $f(x)=y$ For all real $y \neq 2$, there exists $x$ such that $f(x)=y$ None of the above is true
asked Sep 23, 2019 in Calculus Arjun 93 views
0 votes
0 answers
15
Let $f(x)$ be a continuous function from $[0,1]$ to $[0,1]$ satisfying the following properties. $f(0)=0$, $f(1)=1$, and $f(x_1)<f(x_2)$ for $x_1 < x_2$ with $0 < x_1, \: x_2<1$. Then the number of such functions is $0$ $1$ $2$ $\infty$
asked Sep 23, 2019 in Calculus Arjun 170 views
1 vote
2 answers
16
Let $f: \bigg( – \dfrac{\pi}{2}, \dfrac{\pi}{2} \bigg) \to \mathbb{R}$ be a continuous function, $f(x) \to +\infty$ as $x \to \dfrac{\pi^-}{2}$ and $f(x) \to – \infty$ as $x \to -\dfrac{\pi^+}{2}$. Which one of the following functions satisfies the above properties of $f(x)$? $\cos x$ $\tan x$ $\tan^{-1} x$ $\sin x$
asked Sep 23, 2019 in Calculus Arjun 139 views
0 votes
0 answers
17
Let $f(x) = \begin{cases}\mid \:x \mid +1, & \text{ if } x<0 \\ 0, & \text{ if } x=0 \\ \mid \:x \mid -1, & \text{ if } x>0. \end{cases}$ Then $\underset{x \to a}{\lim} f(x)$ exists if $a=0$ for all $a \in R$ for all $a \neq 0$ only if $a=1$
asked Sep 23, 2019 in Calculus Arjun 98 views
0 votes
0 answers
18
Which of the following is true? $\log(1+x) < x- \frac{x^2}{2} + \frac{x^3}{3} \text{ for all } x>0$ $\log(1+x) > x- \frac{x^2}{2} + \frac{x^3}{3} \text{ for all } x>0$ $\log(1+x) > x- \frac{x^2}{2} + \frac{x^3}{3} \text{ for some } x>0$ $\log(1+x) < x- \frac{x^2}{2} + \frac{x^3}{3} \text{ for some } x>0$
asked Sep 23, 2019 in Calculus Arjun 84 views
0 votes
1 answer
19
If $x$ is real, the set of real values of $a$ for which the function $y=x^2-ax+1-2a^2$ is always greater than zero is $- \frac{2}{3} < a \leq \frac{2}{3}$ $- \frac{2}{3} \leq a < \frac{2}{3}$ $- \frac{2}{3} < a < \frac{2}{3}$ None of these
asked Sep 23, 2019 in Calculus Arjun 76 views
0 votes
1 answer
20
Let $f(x) = \dfrac{x}{(x-1)(2x+3)}$, where $x>1$. Then the $4^{th}$ derivative of $f, \: f^{(4)} (x)$ is equal to $- \frac{24}{5} \bigg[ \frac{1}{(x-1)^5} – \frac{48}{(2x+3)^5} \bigg]$ $\frac{24}{5} \bigg[ – \frac{1}{(x-1)^5} + \frac{48}{(2x-3)^5} \bigg]$ $\frac{24}{5} \bigg[ \frac{1}{(x-1)^5} + \frac{48}{(2x+3)^5} \bigg]$ $\frac{64}{5} \bigg[ \frac{1}{(x-1)^5} + \frac{48}{(2x+3)^5} \bigg]$
asked Sep 23, 2019 in Others Arjun 151 views
1 vote
2 answers
21
If two real polynomials $f(x)$ and $g(x)$ of degrees $m\: (\geq 2)$ and $n\: (\geq 1)$ respectively, satisfy $f(x^2+1)=f(x)g(x),$ for every $x \in \mathbb{R}$, then $f$ has exactly one real root $x_0$ such that $f’(x_0) \neq 0$ $f$ has exactly one real root $x_0$ such that $f’(x_0) = 0$ $f$ has $m$ distinct real roots $f$ has no real root
asked Sep 23, 2019 in Quantitative Aptitude Arjun 235 views
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