Relations and F...

Let $$\displaystyle f:R \rightarrow R $$ be defined as $$\displaystyle f(x)= x^{2}+5x+9$$ then $$\displaystyle f^{-1}(8) $$ equals to 

If $$\displaystyle f(x)= (x-1)+(x+1)$$ and
$$\displaystyle g(x)= f\left \{ f(x) \right \}$$ then $$\displaystyle {g}'(3)$$

If $$\displaystyle f\left ( x \right )=x+\tan x$$ and $$\displaystyle g^{-1}=f$$ then $$\displaystyle g{}'\left ( x \right )$$ equals

Let $$\displaystyle f:N\rightarrow Y$$  be a function defined as $$f(x)=4x+3$$ where $$\displaystyle Y=\left \{ y \in N:y=4x+3 \right \}$$ for some $$\displaystyle x\in N$$ such that $$f$$ is invertible then its inverse is

Let f(x)=tan x, x$$\displaystyle \epsilon \left [ -\frac{\pi }{2},\frac{\pi }{2} \right ]$$ and $$\displaystyle g\left (x  \right )=\sqrt{1-x^{2}}$$ Determine $$g o f(1)$$.

If $$\displaystyle f\left ( x \right )=\frac{ax+b}{cx+d}$$ and $$\displaystyle \left ( fof \right )x=x,$$ then d=?

The total number of injective mappings from a set with $$m$$ elements to a set with $$n$$ elements,$$\displaystyle m\leq n,$$ is

Given $$\displaystyle f\left ( x \right )=\log \left ( \frac{1+x}{1-x} \right )$$ and $$\displaystyle g\left ( x \right )=\frac{3x+x^{3}}{1+3x^{2}}, fog (x)$$ equals

The inverse of the function$$\displaystyle f(x)=(1-(x-5)^{3})^{1/5} $$is