Relations and F...

If $$f (x) = x + 2, g (x) = 2 x +3,$$ then find gof

Let $$\displaystyle a > 1$$ be a real number and $$\displaystyle f\left ( x \right ) = \log _{a} x^{2}$$ for $$\displaystyle x > 0$$. If $$\displaystyle f^{-1}$$ is the inverse function of $$f$$ and $$b$$ and $$c$$ are real numbers then $$\displaystyle f^{-1} \left ( b+c \right )$$ is equal to

Which one of the following functions is not one-one?

$$f(x)=x^3+3x^2+4x+b \sin x+c \cos x, \forall x\in R$$ is a one-one function, then the value of $$b^2+c^2$$ is

If $$f(x)=2x+|x|, g(x)=\dfrac {1}{3}(2x-|x|)$$ and $$h(x)=f(g(x))$$, then domain of $$\sin^{-1}\underset {\text {n times}}{\underbrace {(h(h(h(h.....h(x).....))))}}$$ is

Which of the following functions is/are injective map(s) ?

The function $$f$$ is one to one and the sum of all the intercepts of the graph is $$5$$. The sum of all the intercept of the graph $$\displaystyle y = f^{-1} \left ( x \right )$$ is

If $$\displaystyle f \left ( x \right ) = px + q$$ and $$\displaystyle f \left ( f\left ( f\left ( x \right ) \right ) \right ) = 8x + 21$$, where $$p$$ and $$q$$ are real numbers, the $$ p + q$$ equals

Let $$f\left( x \right) =\left\{ \begin{matrix} 1+|x|,\; x<-1 \\ \left[ x \right] ,\; x\ge -1 \end{matrix} \right. $$ where $$[\cdot]$$ denotes the greatest integer function. Then $$\displaystyle f\left \{f(-2.3) \right\}$$ is equal to 

The inverse function of the function $$\displaystyle f(x)=\frac{e^{x}-e^{-x}}{e^{x}+e^{-x}}$$ is