Relations and F...

If $$\displaystyle f:\left ( 3,4 \right )\rightarrow \left ( 0,1 \right )$$ is defined by $$\displaystyle f\left ( x \right )=x-\left [ x \right ]$$ where $$\displaystyle [x] $$denotes the greatest integer function then $$ f^{-1}(x)$$ is

Let $$\displaystyle f(x)=\frac{ax}{x+1}$$, where $$\displaystyle x\neq -1$$. Then for what value of $$\displaystyle a$$ is $$\displaystyle f( f(x))=x$$ always true

Let $$ f:R \rightarrow R$$ and $$g:R \rightarrow R$$ be defined by $$f(x)=x^2+2x-3,g(x)=3x-4$$ then $$(gof) (x)=$$

If $$f(x)=ax+b$$ and $$g(x)=cx+d$$, then $$f(g(x))=g(f(x))$$ implies

If $$f$$ and $$g$$ are two functions such that  $$\displaystyle \left ( fg \right )\left ( x \right )=\left ( gf \right )\left ( x \right )$$ for all $$x$$. Then $$f $$ and $$g$$ may be defined as

If $$f:R\rightarrow R$$ such that $$f(x)=log_3 x$$ then $$f^{-1} x$$ is equal to

If $$f:\left( 3,6 \right) \rightarrow \left( 1,3 \right) $$ is a function defined by $$\displaystyle f\left( x \right)=x-\left[ \frac { x }{ 3 }  \right] $$ $$($$ where $$\left[ . \right] $$ denotes the greatest integer function $$),$$ then $$\displaystyle f^{ -1 }\left( x \right)=$$

Let $$S$$ be a set containing $$n$$ elements. Then the total number of binary operations on $$S$$ is

Let $$f: R\rightarrow R$$ be defined by $$f(x)=3x-4$$ then $$f^{-1}(x)$$ is

A function $$y=f\left ( x \right )$$ is invertible only when