Functions Test ...

The number of one-one functions that can be defined from $$A=\{4,8,12,16\}$$ to $$B$$ is $$5040,$$ then $$n(B)=$$

If $$f:R\rightarrow R, g:R\rightarrow R$$ are defined by $$f(x)=x^{2}, g(x)=\cos x$$  then $$(gof)(x)=$$

Let $$f(x)=\dfrac{Kx}{x+1}(x\neq -1)$$ then the value of $$K$$ for which $$(fof)(x)=x$$ is

If $$n (A) = 4$$ and $$n(B) = 6$$, then the number of surjections from $$A$$ to $$B$$ is

$$f:\left ( -\dfrac{\pi }{2},\dfrac{\pi }{2} \right )\rightarrow \left ( -\infty ,\infty  \right )$$ defined by $$f(x)=1+3x$$ is

Let $$A=\{1,2,3\}, B =\{a, b, c\}$$ and If $$f=\{(1,a),(2,b),(3,c)\}, g=\{(1,b),(2,a),(3,b)\}, h=\{(1,b)(2,c),(3,a)\}$$ then

If $$f:R\rightarrow R, g:R\rightarrow R$$ are defined by $$f(x)=4x-1,g(x)=x^{3}+2,$$ then $$(gof)\left(\dfrac{a+1}{4}\right)=$$ 

If $$f(x)=2x+1$$ and $$g(x)=x^{2}+1$$ then $$ (go(fof))(2)=$$

If $$f:R\rightarrow R,f(x)=3x-2$$ then $$ (fof)(x)+2=$$

If $$f(x)=\dfrac{1}{x}, g(x)=\sqrt{x}$$  and $$ (go\sqrt{f})(16)=$$