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Recent questions tagged ch1

If $A=\{x:x\in R\:\:and\:\:x\geq \large\frac{1}{2}\}$ and $B=\{x:x\in R\:\:and\:\:x\geq\large\frac{3}{4}\}$ and $f:A\rightarrow B$ is defined as $f(x)=x^2-x+1$ so that $f(x)=f^{-1}(x)$ then the solution set of $x$ is ?

asked May 27, 2013 by rvidyagovindarajan_1

1 answer

If $A=\{x:x\in R\:\:and\:\:x\geq \large\frac{1}{2}\}$ and $B=\{x:x\in R\:\:and\:\:x\geq\large\frac{3}{4}\}$ and $f(x)=x^2-x+1$ so that $f(x)=f^{-1}x$ then the solution set of $x$ is ?

asked May 27, 2013 by rvidyagovindarajan_1

0 answers

If $f(x)=x^n$, $n\in N$ and $gof(x)=ng(x)$, then $g(x)$ = ?

asked May 27, 2013 by rvidyagovindarajan_1

1 answer

$If A\{x,y,z\},\:\:B=\{1,2,3\}$ and $f:A\rightarrow B\:\:is\:1-1\:$function. Also one out of the following statements, $f(z)\neq 2,\:\:f(x)=1\:\:and\:\:f(y)\neq 1$ is true. then $f^{-1}(1)=?$

asked May 25, 2013 by rvidyagovindarajan_1

1 answer

If $ A=\{x:x\in R\:and\:x\geq 1\}$ and $ f:A\rightarrow A$ is defined as $f(x)=2^{x(x-1)},$ then find $ f^{-1}(x).$

asked May 25, 2013 by rvidyagovindarajan_1

1 answer

If $f:R\rightarrow R$ is defined as $f(x)=6^x+6^{|x|}$ then what type of function is $f$ ?

asked May 25, 2013 by rvidyagovindarajan_1

1 answer

If $f(X)=\large\frac{kx}{1+x}$, $x\neq1$ and $fof(x)=x$, then find $k$.

asked May 25, 2013 by rvidyagovindarajan_1

1 answer

If $A=\{-1,0,1\}$ and $f:A\rightarrow A$ is defined as $f(x)=x^2$, then what type of function is $f$ ?

asked May 25, 2013 by rvidyagovindarajan_1

1 answer

If $f:R\rightarrow R$ is defined as $f(x)=x^2+1$ then $f^{-1}(x)$ = ?

asked May 24, 2013 by rvidyagovindarajan_1

1 answer

If $f:R\rightarrow R$ is defined as $f(x)=3x-5$, then $f^{-1}(x)$ = ?

asked May 24, 2013 by rvidyagovindarajan_1

1 answer

Range of $f(x)=\large\frac{x-[x]}{1+x-[x]}$ where $[x]$ is greatest integer function.

asked May 21, 2013 by rvidyagovindarajan_1

1 answer

Domain of $f(x)=\large\frac{1}{\sqrt {|x|-x}}$ = ?

asked May 21, 2013 by rvidyagovindarajan_1

1 answer

If $f(x)=\large\frac{x}{x+1},$ $g(x)=\large\frac{x}{1-x}$ and $h(x)=\sqrt [3] {x},$ then $(fogoh)^{-1}(8)= ?$

asked May 21, 2013 by rvidyagovindarajan_1

1 answer

If $g(f(x))=|sinx|$ and $f(g(x))=(sin\sqrt x)^2$ then find $ f(x)\:\: and\:\: g(x)$

asked May 21, 2013 by rvidyagovindarajan_1

1 answer

$A\cap (A\cap B)'$ = ?

asked May 21, 2013 by rvidyagovindarajan_1

1 answer

If $A=\{x:x\in R\:\:and\:\:x\geq 4\}$ and $B=\{x:x\in R\:and\:x< 5\}$, then $A\cap B$ = ?

asked May 21, 2013 by rvidyagovindarajan_1

1 answer

If $A=\{1,3,5,B\}$ and $B=\{2,4\}$, then which of the following is true ?

asked May 21, 2013 by rvidyagovindarajan_1

1 answer

$A\cap (A\cup B)$ = ?

asked May 21, 2013 by rvidyagovindarajan_1

1 answer

If $log_2(log_3(log_4(log_5x)))=0$ then x= ?

asked May 18, 2013 by rvidyagovindarajan_1

1 answer

If $S_1=\{1,2,...................20\}$, $S_2=\{a,b,c,d,e\}$, $S_3=\{a,c,e,f\}$, then no. of elements of $(S_1\times S_2)\cap (S_1\times S_3)$ is ?

asked May 18, 2013 by rvidyagovindarajan_1

1 answer

If $f(x)=\cos \log x$ then $f(x).f(y)-\large\frac{1}{2}$$\bigg(f(\large\frac{x}{y}$)$+f(xy)\bigg)= ?$

asked May 18, 2013 by rvidyagovindarajan_1

1 answer

The set that cannot be represented by roster form is:

asked May 17, 2013 by rvidyagovindarajan_1

1 answer

How is Null set represented in set builder form ?

asked May 17, 2013 by rvidyagovindarajan_1

1 answer

If $A\cap B=B$ then what can you say about $A$ and $B $?

asked May 17, 2013 by rvidyagovindarajan_1

1 answer

If $A\cup B=A,\:\:$ then what can you say about $A$ and $B$?

asked May 17, 2013 by rvidyagovindarajan_1

1 answer

If $A,B\:and\: C$ are three finite sets, then $[(A\cup B)\cap C]' $ = ?

asked May 15, 2013 by rvidyagovindarajan_1

1 answer

How many proper subsets are there for a set having 5 elements ?

asked May 15, 2013 by rvidyagovindarajan_1

1 answer

If $V=\{x:\:x+2=0\}$, $\:R=\{x:\:x^2+2x=0\}$ and $\:\:S=\{x:\:x^2+x-2=0\}$, then for what value of $x$, $V=R=S$ ?

asked May 15, 2013 by rvidyagovindarajan_1

1 answer

If $f:R\rightarrow R$ is defined $f(x)=x^2-3$ then $f^{-1}x$ = ?

asked May 13, 2013 by rvidyagovindarajan_1

1 answer

$f:N\rightarrow Z$ is a function defined as $f(n)=\left\{ \begin {array} {1 1} \large\frac{n-1}{2}, \:\:when\:\: n\:\: is\:\: odd \\ -\large \frac{n}{2},\:\:when\:\: n\:\: is\:\: even \\ \end{array} \right.$, then $f$ is

asked May 13, 2013 by rvidyagovindarajan_1

1 answer

If $M$ is the set of all $2\times 2$ matrices with real entries and $f :M\rightarrow R$ is defined as $ f(A)=|A| \:\forall\:A\in M$, then $f$ is

asked May 12, 2013 by rvidyagovindarajan_1

1 answer

If $g(x)=1+x-[x]$ where $[x]$ is greatest integer $x$ and $f(x)=\left\{\begin{array}{111}-1,\:\:\:\:x<0\\0,\:\:\:\:\:x=0\\1,\:\:\:\:\:x>0\end{array}\right.$ then $fog(x)=?$

asked May 12, 2013 by rvidyagovindarajan_1

1 answer

If $f(x)=x^2\:\:and\:\:g(x)=2^x$ and $fog(x)=gof(x)$ then $x$ = ?

asked May 12, 2013 by rvidyagovindarajan_1

1 answer

If $f(x)=\large\frac{1}{1-x}$ is a function defined in $R-\{1\}$ then $\;fofof(x)$ = ?

asked May 12, 2013 by rvidyagovindarajan_1

1 answer

If $$ is a binary operation defined as $ab=3a-b$, then $(23)4=$ ?

asked May 12, 2013 by rvidyagovindarajan_1

1 answer

If * is a binary operation defined in $Q^+$ as $ab=\large\frac{ab}{3}$, then the inverse element of 46 is ?

asked May 12, 2013 by rvidyagovindarajan_1

1 answer

If * is a binary operation defined by a*b=$\frac{ab}{100}$ in $Q^+$ then the inverse element of 0.1 is:

asked May 12, 2013 by rvidyagovindarajan_1

1 answer

If $f(x)=x^2$ $g(x)=sinx$, $\forall x\in R$, then the set of all $x$ satisfying $fogogof(x)=gogof(x)$ is

asked May 7, 2013 by rvidyagovindarajan_1

1 answer

If $f(x)$ is a real valued function satisfying $f(x+1)+f(x-1)=2f(x)$ $\forall x\in R$ and $f(0)=0$, then for any $n\in N,\:f(n)$ = ?

asked May 7, 2013 by rvidyagovindarajan_1

1 answer

The domain of $y=sin^{-1}(1+3x+2x^2)$ is

asked May 7, 2013 by rvidyagovindarajan_1

1 answer

If $A\:and\:B$ are two sets such that $(A-B)\cup B=A$, then what can you say about $A\:and\:B$?

asked May 4, 2013 by rvidyagovindarajan_1

1 answer

If $f:R\rightarrow S$ defined by $\:f(x)=\sin x-\sqrt3\; \cos x+1\;$ is onto function then $S$ = ?

asked May 4, 2013 by rvidyagovindarajan_1

1 answer

If $f$ is a real values function satisfying $f(x+y)=f(x)\;f(y)$ and $f(1)=a$ where $x,y\in R$, then $f(x)$ =

asked May 4, 2013 by rvidyagovindarajan_1

1 answer

The value of $\alpha$ for which the function $f(x)=1+\alpha x,\:\:\alpha\neq 0$ is the inverse of itself is:

asked May 4, 2013 by rvidyagovindarajan_1

1 answer

The inverse of $f(x)=x-[x],$ where $[x]$ is greatest integer function is

asked May 2, 2013 by rvidyagovindarajan_1

2 answers

What is the inverse of the function $f(x)=\large\frac{e^x-e^{-x}}{e^x+e^{-x}}$

asked May 2, 2013 by rvidyagovindarajan_1

1 answer

The no. of subsets of a finite set A is 56 more than the no. of subsets of another finite set B. What is the no. of elements of A?

asked May 1, 2013 by rvidyagovindarajan_1

1 answer

If $A=\{1,2,3\}$ then the no. of relations in $A$ containing $(1,2)$ and $(1,3)$ which are reflexive and symmetric but not transitive is

asked May 1, 2013 by rvidyagovindarajan_1

1 answer

If * is binary operation defined in N as ab=$a^3+b^3$ then is

asked May 1, 2013 by rvidyagovindarajan_1

1 answer

If n(A) = 4, n(B) = 6, then the number of 1-1 functions from A to B is

asked May 1, 2013 by rvidyagovindarajan_1

1 answer

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