Functions Test ...

A function $$f$$ from the set of natural numbers to integers defined by $$f(n)=\begin{cases} \cfrac { n-1 }{ 2 } ,\quad \text{when n is odd} \\ -\cfrac { n }{ 2 } ,\quad \text{when n is even} \end{cases}$$  is

Let $$f:Z\rightarrow Z$$ be given by $$f(x)=\begin{cases} \cfrac { x }{ 2 } ,\quad \text{if}\ x \ \text{is even} \\ 0,\quad \text{if }\ x \ \text{is odd} \end{cases}$$. Then, $$f$$ is

If $$g(x)={ x }^{ 2 }+x-2$$ and $$\cfrac { 1 }{ 2 } (g\circ f(x))=2{ x }^{ 2 }-5x+2$$, then $$f(x)$$ is equal to

A function $$f$$ from the set of natural numbers to the set of integers defined by
$$f(n)=\begin{cases} \cfrac { n-1 }{ 2 } ,\quad \text{when n is odd} \\ -\cfrac { n }{ 2 } ,\quad \text{when n is even} \end{cases}$$

Let $$M$$ be the set of all $$2\times 2$$ matrices with entries from the set $$R$$ of real numbers. Then the function $$f:M\rightarrow R$$ defined by $$f(A)=\left| A \right| $$ for every $$A\in M$$, is

The function $$f:R\rightarrow R$$ defined by $$f(x)=(x-1)(x-2)(x-3)$$ is

Let $$S$$ be the set of all real roots of the equation, $${ 3 }^{ x }\left( { 3 }^{ x }-1 \right) +2=\left| { 3 }^{ x }-1 \right| +\left| { 3 }^{ x }-2 \right| $$. Then $$S$$:

If $$f(x) = \dfrac{x+1}{x-1}$$, then the valueof $$f(f(x))$$ is equal to

Let $$f : x \rightarrow y $$ be such that $$f(1) = 2$$ and $$f(x + y) = f(x) f(y)$$ for all natural numbers x and y. If $$\displaystyle \sum_{k= 1}^n f(a + k) = 16 (2^n - 1)$$ , then a is equal to 

If $$f(x)=\dfrac{(4x+3)}{(6x-4)}, x\neq \dfrac{2}{3}$$ then $$(f o f)(x)=?$$