Relations and F...

Let $$\displaystyle f:(-\infty,1]\rightarrow (-\infty,1]$$ such that $$\displaystyle f(x)=x(2-x).$$ Then $$f^{-1}(x)$$ is

If $$\displaystyle f(x)=\frac{1}{1-x},x\neq 0,1$$ then the graph of the function $$\displaystyle y=f\left \{ f(f(x)) \right \},x> 1,$$ is

Let $$\displaystyle f:\left \{ x,y,z \right \}\rightarrow \left \{ a,b,c \right \}$$ be a one-one function and only one of the conditions $$(i)f(x)\neq b, (ii)f(y)=b,(iii)f(z)\neq a$$ is true then the function $$f$$  is given by the set 

If $$\displaystyle f(x)=3x-5$$ then $$f^{-1}(x)=$$

Which of the following function is one-one?

If $$\displaystyle f(x)=x^{n},n\in N$$ and $$(gof)(x)=ng(x)$$ then $$g(x)$$ can be 

If $$f:R^+\rightarrow A$$, Where $$A=\{x:-5<x<\infty\}$$ be defined by $$f(x)=x^2-5$$. Then $$f^{-1}(7)=$$

If the function $$f:[1,\infty)\rightarrow [1,\infty)$$ is defined by $$\displaystyle f(x)=3^{x(x-1)}$$ then $$f^{-1}(x) $$ is 

The composite mapping $$fog$$ of the map $$f: R\rightarrow R,f(x)=\sin x$$ and $$g: R\rightarrow R, g(x)=x^2$$ is

If the function $$f:R\rightarrow R$$ be such that $$\displaystyle f(x)=x-[x],$$ where $$[y]$$ denotes the greatest integer less than or equal to $$y$$, then $$f^{-1}(x)$$ is