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Recent questions tagged functions
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1
TIFR ECE 2014 | Question: 13
Let function $f: \mathbf{R} \rightarrow \mathbf{R}$ be convex, i.e., for $x, y \in \mathbf{R}, \alpha \in[0,1], f(\alpha x+(1-\alpha) y) \leq$ $\alpha f(x)+(1-\alpha) f(y)$. Then which of the following is $\text{TRUE?}$ $f(x) \leq f(y)$ whenever ... $f$ and $g$ are both convex, then $\min \{f, g\}$ is also convex. For a random variable $X, E(f(X)) \geq f(E(X))$.
admin
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Calculus
Dec 14, 2022
by
admin
43.6k
points
16
views
tifr2014
calculus
functions
1
vote
0
answers
2
TIFR ECE 2013 | Question: 20
A function $f: \mathbb{R} \rightarrow \mathbb{R}$ is convex if for $x, y \in \mathbb{R}, \alpha \in[0,1], f(\alpha x+(1-\alpha) y) \leq \alpha f(x)+(1-\alpha) f(y)$. Which of the following is not convex: $x^{2}$ $x^{3}$ $x$ $x^{4}$ $\mathrm{e}^{x}$
admin
asked
in
Calculus
Dec 12, 2022
by
admin
43.6k
points
10
views
tifr2013
calculus
functions
1
vote
0
answers
3
TIFR ECE 2019 | Question: 5
Consider the function $f(x)=e^{x^{2}}-8 x^{2}$ for all $x$ on the real line. For how many distinct values of $x$ do we have $f(x)=0?$ $1$ $4$ $2$ $3$ $5$
admin
asked
in
Calculus
Nov 30, 2022
by
admin
43.6k
points
6
views
tifrece2019
calculus
functions
1
vote
0
answers
4
TIFR ECE 2017 | Question: 6
Let $a, b \in\{0,1\}$. Consider the following statements where $*$ is the $\text{AND}$ operator, $\oplus$ is $\text{EXCLUSIVE-OR,}$ and ${ }^{c}$ denotes the complement function. $\max \left\{a * b, b \oplus a^{\mathrm{c}}\right\}=1$ ... $\text{(iii)}$ only $\text{(iii)}$ and $\text{(iv)}$ only $\text{(iv)}$ and $\text{(i)}$ only None of the above
admin
asked
in
Calculus
Nov 29, 2022
by
admin
43.6k
points
12
views
tifrece2017
calculus
functions
1
vote
2
answers
5
GATE ECE 2020 | GA Question: 5
A superadditive function $f(\cdot)$ satisfies the following property $f\left ( x_{1} +x_{2}\right )\geq f\left ( x_{1} \right ) + f\left ( x_{2} \right )$ Which of the following functions is a superadditive function for $x > 1$? $e^{x}$ $\sqrt{x}$ $1/x$ $e^{-x}$
go_editor
asked
in
Quantitative Aptitude
Feb 13, 2020
by
go_editor
1.9k
points
979
views
gate2020-ec
numerical-ability
functions
0
votes
0
answers
6
GATE ECE 2016 Set 2 | Question: 4
How many distinct value of $x$ satisfy the equation $\sin(x)=x/2$, where $x$ is in radians? $1$ $2$ $3$ $4$ or more
Milicevic3306
asked
in
Calculus
Mar 28, 2018
by
Milicevic3306
15.8k
points
68
views
gate2016-ec-2
calculus
functions
0
votes
0
answers
7
GATE ECE 2015 Set 1 | Question: 28
Which one of the following graphs describes the function $f(x)=e^{-x}(x^2+x+1)$?
Milicevic3306
asked
in
Calculus
Mar 28, 2018
by
Milicevic3306
15.8k
points
57
views
gate2015-ec-1
calculus
functions
0
votes
0
answers
8
GATE ECE 2014 Set 4 | GA Question: 4
Let $f(x,y)=x^n y^m=P$. If $x$ is doubled and $y$ is halved, the new value of $f$ is $2^{n-m}P$ $2^{m-n}P$ $2(n-m)P$ $2(m-n)P$
Milicevic3306
asked
in
Quantitative Aptitude
Mar 26, 2018
by
Milicevic3306
15.8k
points
47
views
gate2014-ec-4
numerical-ability
functions
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