Relations and F...

Let f be injective map with domain {x , y, z} and range {1, 2, 4} such the exactly one of the following statement is correct and the remaining are false $$f(x)=1,f(y)\neq 1,f(z)\neq 2$$ then \\ $${ f }^{ -1 }(1)$$

Let a, b, c be real numbers with 0 < a < 1, 0 < b < 1, 0 < c < 1 and a + b + = 2 then$$\dfrac{a}{1 - a}$$,$$\dfrac{b}{1 - b}$$, $$\dfrac{c}{1 - c}$$

If $$y^2 = ax^2 +bx+c$$, then $$y^2 \dfrac{d^2y}{dx^2}$$ is

Let f be a differential function satisfying the relation f(xy) = xf(y) +yf(x) -2xy (wherer x,y > 0) and f(1) = 3 then 

if $$\left( x \right) =\sqrt { { x+2 }\sqrt { 2x-4 }  } +\sqrt { { x-2 }\sqrt { 2x-4 }  } $$ then the value of $$10 { f }^{ 1 }\left( { 102 }^{ + } \right)$$

Let $$f(1)=1$$ and $$f(n)=2\sum_{r=1}^{n-1}{f(r)}$$. Then $$\sum_{n=1}^{m}{f(n)}$$. is equal to 

If $$f(x) = \dfrac{cos \, x}{(1 - sin x)}^{1/3}$$ then

$$f(x) = e^x \sin x$$, then $$f^n(x)$$ is equal to

If $$2f(x-1)-f\left(\dfrac{1-x}{x}\right)=x$$, then $$f(x)$$ is 

Let $$f(x)=(x+1)^{2}-1, x\ge -1$$. Then the set $$\left\{x: f(x)=f^{-1}(x)\right\}$$ is