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Recent questions tagged functions

1 1 vote
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ISI2016-DCG-36
Suppose $X$ and $Y$ are finite sets, each with cardinality $n$.. The number of bijective functions from $X$ to $Y$ is$n^{n}$$n\log_{2}n$$n^{2}$$n!$
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442
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ISI2016-DCG-37
Suppose $f_{\alpha}\::\:[0,1]\rightarrow[0,1],\:-1<\alpha<\infty$ is given by$$f_{\alpha}(x)=\dfrac{(\alpha+1)x}{\alpha x+1}.$$Then $f_{\alpha}$ isA bijective (one-one an...
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1 1 answer
720
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ISI2016-DCG-48
The piecewise linear function for the following graph is$f(x)=\begin{cases} = x,x\leq-2 \\ =4,-2<x<3 \\ = x+1,x\geq 3\end{cases}$$f(x)=\begin{cases} = x-2,x\leq-2 \\ =4,...
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1 1 vote
1 1 answer
651
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ISI2016-DCG-50
The domain of the function $\ln(3x^{2}-4x+5)$ isset of positive real numbersset of real numbersset of negative real numbersset of real numbers larger than $5$
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628
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ISI2016-DCG-58
Let $y=\left \lfloor x \right \rfloor$ where $\left \lfloor x \right \rfloor$ is greatest integer less than or equal to $x$. Then$y$ is continuous and many-one.$y$ is not...
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2 2 votes
1 1 answer
672
672 views
ISI2017-DCG-3
If $2f(x)-3f(\frac{1}{x})=x^2 \: (x \neq0)$, then $f(2)$ is$\frac{2}{3}$$ – \frac{3}{2}$$ – \frac{7}{4}$$\frac{5}{4}$
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0 0 votes
1 1 answer
1.4k
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ISI2017-DCG-6
Let $f(x) = \dfrac{x-1}{x+1}, \: f^{k+1}(x)=f\left(f^k(x)\right)$ for all $k=1, 2, 3, \dots , 99$. Then $f^{100}(10)$ is$1$$10$$100$$101$
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1 1 vote
2 2 answers
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ISI2017-DCG-30
If $f(x)=e^{5x}$ and $h(x)=f’’(x)+2f’(x)+f(x)+2$ then $h(0)$ equals$38$$8$$4$$0$
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2 2 votes
1 1 answer
1.1k
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ISI2018-DCG-9
Let $f(x)=1+x+\dfrac{x^2}{2}+\dfrac{x^3}{3}...+\dfrac{x^{2018}}{2018}.$ Then $f’(1)$ is equal to $0$$2017$$2018$$2019$
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0 0 votes
1 1 answer
565
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ISI2018-DCG-28
Let $f(x)=e^{-\big( \frac{1}{x^2-3x+2} \big) };x\in \mathbb{R} \: \: \& x \notin \{1,2\}$. Let $a=\underset{n \to 1^+}{\lim}f(x)$ and $b=\underset{x \to 1^-}{\lim} f(x)$....
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3 3 votes
1 1 answer
1.9k
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UGC NET CSE | June 2019 | Part 2 | Question: 13
How many different Boolean functions of degree $n$ are the$2^{2^n}$$(2^2)^n$$2^{2^n} -1$$2^n$
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13 13 votes
3 answers 3 answers
2.9k
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GATE2010 TF: GA-5
Consider the function $f(x)=\max(7-x,x+3).$ In which range does $f$ take its minimum value$?$ $-6\leq x<-2$ $-2\leq x<2$ $2\leq x<6$$6\leq x<10$
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5 5 votes
1 answers 1 answer
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GATE2010 MN: GA-10
Given the following four functions $f_{1}(n)=n^{100},$ $f_{2}(n)=(1.2)^{n},$ $f_{3}(n)=2^{n/2},$ $f_{4}(n)=3^{n/3}$ which function will have the largest value for suffi...
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1 1 vote
1 1 answer
877
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ISI2018-PCB-CS3
An $n-$variable Boolean function $f:\{0,1\}^n \rightarrow \{0,1\} $ is called symmetric if its value depends only on the number of $1’s$ in the input. Let $\sigma_n $ den...
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4 4 votes
1 1 answer
2.2k
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ISI2019-MMA-30
Consider the function $h$ defined on $\{0,1,…….10\}$ with $h(0)=0, \: h(10)=10 $ and$$2[h(i)-h(i-1)] = h(i+1) – h(i) \: \text{ for } i = 1,2, \dots ,9.$$Then the val...
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0 0 votes
1 1 answer
952
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Michael Sipser Edition 3 Exercise 0 Question 6 (Page No. 26)
Let X be the set {1, 2, 3, 4, 5} and Y be the set {6, 7, 8, 9, 10}. The unary function$ f: X→Y$ and the binary function $g: X × Y →Y$ are described in the following table...
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0 0 votes
1 answers 1 answer
853
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finding two positive integers in an array
I'm facing a problem these days, the question is saying the following: " Imagine we are having an array of positive integers called (a) and a variable called (k). Among t...
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0 0 votes
1 answers 1 answer
1.1k
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Functions and Relations
What is the number of relations S over set {0,1,2,3} such that (x,y) $\epsilon$ S $\Rightarrow x = y$ ? Thanks.
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0 0 votes
1 answers 1 answer
893
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Functions
What Is The Total Number Of Boolean Functions Possible Over N Boolean Variables?
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3.9k
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Composition of a relation- Madeeasy 2019
How to take composition of a Relation? here used concept of function but when to go with the transitivity rule concept as mentioned below?Please clarify in general when t...
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1.2k
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Function Pointer question
#include<stdio.h>int main ( ){ int demo ( ); // What is this and what does it do? demo ( ); (*demo) ( );}int demo ( ){ printf("Morning");}
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1 1 vote
0 0 answers
1.4k
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Zeal Test Series 2019: Set Theory & Algebra - Functions
I think only d) is correct
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3 3 votes
2 2 answers
1.6k
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TIFR CSE 2019 | Part A | Question: 6
A function $f: \mathbb{R} \rightarrow \mathbb{R}$ is said to be $\textit{convex}$ if for all $x,y \in \mathbb{R}$ and $\lambda$ such that $0 \leq \lambda \leq1,$ $f(...
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3 3 votes
1 1 answer
2.6k
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TIFR CSE 2019 | Part A | Question: 12
Let $f$ be a function with both input and output in the set $\{0,1,2, \dots ,9\}$, and let the function $g$ be defined as $g(x) = f(9-x)$. The function $f$ is non-decreas...
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1 1 vote
0 0 answers
727
727 views
Floor and Ceil
Is below always true?$\lceil 2x \rceil=2.\lceil x \rceil$
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4 4 votes
2 answers 2 answers
3.2k
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What is the return value of following function for 484? What does it to in general?
What is the return value of following function for 484? What does it to in general?bool fun(int n){ int sum = 0; for (int odd = 1; n sum; odd = odd+2) sum = ...
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0 0 votes
0 0 answers
463
463 views
Function return type
Are these return types valid for a function in C? Would any of these result in error, or simply will be ignored?1 const void f()2 extern void f()3 static void f()
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2 2 votes
1 1 answer
2.4k
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Kenneth Rosen Edition 6th Exercise 2.3 Question 35 (Page No. 147)
Show that the function f(x) = ax + b from R->R is invertible, where a and b are constants, with a$\neq$0, and find the inverse of fHow to check whether this function is o...
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5 5 votes
1 answers 1 answer
3.1k
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Zeal Test Series 2019: Set Theory & Algebra - Functions
Let f : A → B be function, where A = {1,2,3,4,5,6} and B = {1,2,3,4,5}.If f(1) = 4 then how many surjective (onto) functions are possible ?
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