Relations and F...

If $$f(x) = 2x - 6$$, then $$f^{-1}(x)$$ is

If $$f(x) = 4/\sqrt [3]{x + 1}$$, what is $$f^{-1}(7)$$?

Let f : $$N \rightarrow N$$ defined by $$f(n)=\left\{\begin{matrix}
\dfrac{n+1}{2} & \text{if }\, n \, \text{is odd} \\
\dfrac{n}{2} & \text{if}\, n \, \text{is even}
\end{matrix}\right.$$
then $$f$$ is.

If the operation $$\oplus$$ is defined by $$a\oplus b = a^{2} + b^{2}$$ for all real numbers $$'a'$$ and $$'b'$$, the $$(2\oplus 3)\oplus 4 = $$ 

If $$f: R\rightarrow R$$ is defined by $$f(x) = \dfrac {x}{x^{2} + 1}$$, find $$f(f(2))$$

If $$f : IR \rightarrow IR$$ is defined by $$f(x) = 2x + 3$$, then $$f^{-1}(x)$$

If the function $$f : R \rightarrow R$$ is defined by $$f(x) = (x^2+1)^{35} \forall \in R$$, then $$f$$ is

Let $$f(x) = 2^{100}x+1$$
$$g(x) = 3^{100}x+1$$
Then the set of real numbers x such that $$f(g(x)) = x$$ is

The Set $$A$$ has $$4$$ elements and the Set $$B$$ has $$5$$ elements then the number of injective mappings that can be defined from $$A$$ to $$B$$ is

Let $$f : R\rightarrow R$$ be defined by $$f(x) = \dfrac {1}{x} \ \   \forall  \ x \ \in \ R$$, then $$f$$ is _____