Relations and F...

Find the number of binary operations on the set $$\left \{a, b\right \}$$ 

If $$f(x)={2}^{100}x+1, g(x)={3}^{100}x+1$$, then the set of real numbers $$x$$ such that $$f\left\{ g(x) \right\} =x$$ is

In three element group $$\{e, a, b\}$$ where $$e$$ is the identity, $$a^5b^4$$ is equal to 

Find the value of $${f}^{-1}(1.5)$$ if $$f(x)=\sqrt [ 3 ]{ { x }^{ 3 }+1 } $$.

If $$f(x)\, =\, (p\, -\, x^n)^{1/n},\, p\, >\, 0$$ and $$n$$ is a positive integer, then $$f(f(x)) =$$

If $$\displaystyle { Q }_{ 1 }$$ is the set of all relations other than $$1$$ with the binary operation $$\displaystyle \ast $$ defined by $$\displaystyle a\ast b=a+b-ab$$ for all $$a, b \in \displaystyle Q_1$$, then the identity in $$\displaystyle { Q }_{ 1 }$$ with respect to $$\displaystyle { Q }_{ 1 }$$ is

Which of the following is a subgroup of the group $$G = \left \{1, 2, 3, 4, 5, 6\right \}$$ under $$\otimes_{7}$$.

If $$f: R\rightarrow R^{+}$$ and $$g: R^{+} \rightarrow R$$ are such that $$g(f(x)) = |\sin x|$$ and $$f(g(x)) = (\sin \sqrt {x})^{2}$$, then a possible choice for f and g is

In $$Z$$, the set of all integers, the inverse of $$-7$$ w.r.t. defined by $$a\times b=a+b+7$$ for all $$a, b, \in Z$$ is : 

Let Q be the set of all rational numbers in [0, 1] and $$f : [0, 1]\rightarrow [0, 1]$$ be defined by $$f(x)=\begin{cases}x&for&x\in Q\\ 1-x&for&x\notin Q\end{cases}$$
Then the set $$S=\{x\in [0, 1]: (f\, o \, f)(x)=x\}$$ is equal to