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Recent questions tagged functions

1 votes
1 answer
121
JEST 2020
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.
X AND Y is an arbitrary sets, F: $X\rightarrow Y$ show that a and b are equivalent F is one-oneFor all set Z and function g1: $Z\rightarrow X$ and g2: $Z\rightarrow X$, ...
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3 votes
1 answer
123
GATE Civil 2020 Set 2 | GA Question: 5
If $f(x) = x^2$ for each $x\in (-\infty,\infty)$, then $\large \dfrac{f\left(f\left(f(x)\right)\right)}{f(x)}$ is equal to _______. $f(x)$ $(f(x))^2$ $(f(x))^3$ $(f(x))^4$
If $f(x) = x^2$ for each $x\in (-\infty,\infty)$, then $\large \dfrac{f\left(f\left(f(x)\right)\right)}{f(x)}$ is equal to _______.$f(x)$$(f(x))^2$$(f(x))^3$$(f(x))^4$
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2 votes
2 answers
126
ISI2014-DCG-6
If $f(x)$ is a real valued function such that $2f(x)+3f(-x)=15-4x$, for every $x \in \mathbb{R}$, then $f(2)$ is $-15$ $22$ $11$ $0$
If $f(x)$ is a real valued function such that $2f(x)+3f(-x)=15-4x$, for every $x \in \mathbb{R}$, then $f(2)$ is$-15$$22$$11$$0$
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2 votes
3 answers
127
ISI2014-DCG-7
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
If $f(x) = \dfrac{\sqrt{3} \sin x}{2+\cos x}$, then the range of $f(x)$ isthe interval $[-1 , \sqrt{3}{/2}]$the interval $[-\sqrt{3}{/2}, 1]$the interval $[-1, 1]$none of...
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1 votes
1 answer
128
ISI2014-DCG-21
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
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 $x$....
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0 votes
1 answer
129
ISI2014-DCG-24
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
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 $y \neq 1$, ...
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1 votes
0 answers
130
ISI2014-DCG-33
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 $0$ $1$ $2$ $\infty$
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_...
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0 votes
0 answers
132
ISI2014-DCG-43
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 $a=1$
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}...
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0 votes
1 answer
134
ISI2014-DCG-48
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
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}$$- \frac{2}{3} ...
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0 votes
1 answer
135
ISI2014-DCG-49
Let $f(x) = \dfrac{x}{(x-1)(2x+3)}$, where $x>1$. Then the $4^{th}$ derivative of $f, \: f^{(4)} (x)$ is equal to $- \frac{24}{5} \bigg[ \frac{1}{(x-1)^5} - \frac{48}{(2x+3)^5} \bigg]$ ... $\frac{64}{5} \bigg[ \frac{1}{(x-1)^5} + \frac{48}{(2x+3)^5} \bigg]$
Let $f(x) = \dfrac{x}{(x-1)(2x+3)}$, where $x>1$. Then the $4^{th}$ derivative of $f, \: f^{(4)} (x)$ is equal to$- \frac{24}{5} \bigg[ \frac{1}{(x-1)^5} – \frac{48}{(2...
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1 votes
1 answer
139
ISI2015-MMA-33
If $f(x)$ is a real valued function such that $2f(x)+3f(-x)=15-4x,$ for every $x \in \mathbb{R}$, then $f(2)$ is $-15$ $22$ $11$ $0$
If $f(x)$ is a real valued function such that $$2f(x)+3f(-x)=15-4x,$$ for every $x \in \mathbb{R}$, then $f(2)$ is$-15$$22$$11$$0$
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0 votes
1 answer
140
ISI2015-MMA-34
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 the above
If $f(x) = \dfrac{\sqrt{3}\sin x}{2+\cos x}$, then the range of $f(x)$ isthe interval $[-1, \sqrt{3}/2]$the interval $[- \sqrt{3}/2, 1]$the interval $[-1, 1]$none of the ...
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1 votes
1 answer
141
ISI2015-MMA-36
For non-negative integers $m$, $n$ define a function as follows $f(m,n) = \begin{cases} n+1 & \text{ if } m=0 \\ f(m-1, 1) & \text{ if } m \neq 0, n=0 \\ f(m-1, f(m,n-1)) & \text{ if } m \neq 0, n \neq 0 \end{cases}$ Then the value of $f(1,1)$ is $4$ $3$ $2$ $1$
For non-negative integers $m$, $n$ define a function as follows$$f(m,n) = \begin{cases} n+1 & \text{ if } m=0 \\ f(m-1, 1) & \text{ if } m \neq 0, n=0 \\ f(m-1, f(m,n-1))...
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1 votes
1 answer
142
ISI2015-MMA-37
Let $a$ be a non-zero real number. Define $f(x) = \begin{vmatrix} x & a & a & a \\ a & x & a & a \\ a & a & x & a \\ a & a & a & x \end{vmatrix}$ for $x \in \mathbb{R}$. Then, the number of distinct real roots of $f(x) =0$ is $1$ $2$ $3$ $4$
Let $a$ be a non-zero real number. Define$$f(x) = \begin{vmatrix} x & a & a & a \\ a & x & a & a \\ a & a & x & a \\ a & a & a & x \end{vmatrix}$$ for $x \in \mathbb{R}$....
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1 votes
1 answer
144
ISI2015-DCG-27
If $A$ be the set of triangles in a plane and $R^{+}$ be the set of all positive real numbers, then the function $f\::\:A\rightarrow R^{+},$ defined by $f(x)=$ area of triangle $x,$ is one-one and into one-one and onto many-one and onto many-one and into
If $A$ be the set of triangles in a plane and $R^{+}$ be the set of all positive real numbers, then the function $f\::\:A\rightarrow R^{+},$ defined by $f(x)=$ area of t...
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3 votes
1 answer
145
ISI2015-DCG-36
Suppose $X$ and $Y$ are finite sets, each with cardinality $n$. The number of bijective functions from $X$ to $Y$ is $n^n$ $n \log_2 n$ $n^2$ $n!$
Suppose $X$ and $Y$ are finite sets, each with cardinality $n$. The number of bijective functions from $X$ to $Y$ is$n^n$$n \log_2 n$$n^2$$n!$
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1 votes
2 answers
147
ISI2015-DCG-49
The domain of the function $\text{ln}(3x^2-4x+5)$ is set of positive real numbers set of real numbers set of negative real numbers set of real numbers larger than $5$
The domain of the function $\text{ln}(3x^2-4x+5)$ isset of positive real numbersset of real numbersset of negative real numbersset of real numbers larger than $5$
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0 votes
1 answer
149
ISI2016-DCG-27
If $A$ be the set of triangles in a plane and $R^{+}$ be the set of all positive real numbers, then the function $f\::\:A\rightarrow R^{+},$ defined by $f(x)=$ area of triangle $x,$ is one-one and into one-one and onto many-one and onto many-one and into
If $A$ be the set of triangles in a plane and $R^{+}$ be the set of all positive real numbers, then the function $f\::\:A\rightarrow R^{+},$ defined by $f(x)=$ area of t...
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0 votes
1 answer
150
ISI2016-DCG-36
Suppose $X$ and $Y$ are finite sets, each with cardinality $n$.. The number of bijective functions from $X$ to $Y$ is $n^{n}$ $n\log_{2}n$ $n^{2}$ $n!$
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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