Let $$f(x)=(x+2)^2-2, x \geq-2$$. Then, $$f^{-1}(x)$$ is equal to

If $$f$$ is the greatest integers function defined on $$R$$ as $$f(x)=[x]$$ and $$g$$ is the modulus function defined on $R$ as $$g(x)=|x|$$, then the value of $$(g \circ f)\left(\frac{-5}{3}\right)$$ is

If $$f: R \rightarrow R$$ and $$g: R \rightarrow R$$ are two functions defined by $$f(x)=a x+b(a \neq 0), \forall x \in R$$ and $$g(x)=c x^3+d(c \neq 0), \forall x \in R$$, then $$(f \circ g)^{-1}(x)$$ is equal to

Using mathematical induction, the numbers $$a_n^{\prime}$$ s are defined by $$a_0=1, a_{n+1}=3 n^2+n+a_n (n \geq 0)$$, then $$a_n$$ is equal to