Functions Test ...

A real valued function $$f(x)$$ satisfies the function equation $$f(x-y)=f(x)f(y)-f(a-x)f(a+y)$$ where a is a given constant and $$f(0)=1, f(2a-x)$$ is equal to?

Let $$f\left( x \right)={2^{10}}x + 1$$ and $$g\left( x \right) = {3^{10}}x - 1$$ , If $$\left( {fog} \right)\left( x \right) = x$$ , then $$x$$ is equal to

$$f : R^+ \rightarrow R$$ defined by $$f(x) = 2^x , \, x \in (0, 1), \, f(x) = 3^x , \, x \in [1, \, \infty)$$ is 

If $$f(x)=1+|x-1|,-1 \le x \le 3$$ and $$g(x)=2-|x+1|,-2 \le x \le 2$$ then choose the appropriate option.

If $$f(x)=|x|$$ and $$g(x)=[x]$$, then value of $$fog \left(-\dfrac {1}{4}\right)+gof \left(-\dfrac {1}{4}\right)$$ is  ?

The function $$f : R\rightarrow R$$ given by, then $$f(x)=3-2\sin x$$ is

Let $$f(x)=\dfrac{x^{2}-4}{x^{2}+4}$$ for $$|x|>2$$, then the function $$f:(-\infty, -2)\cup [2,\infty)\rightarrow (-1,1)$$ is

If $$f\left( x \right)  = \sin ^{ 2 }{ x } + \sin ^{ 2 }({ { x }+\frac { \pi  }{ 3 })  + \cos { x\cos { \left( { x } + \frac { \pi  }{ 3 }  \right),  ~g(\frac { 5 }{ 4 })  = 1, \text{then} \left( gof \right)\left( x \right)  }  }\ \text{ is}\  \text{equal}\  \text{to}  } $$

$$f:A \rightarrow A,A=\left\{a_{1},a_{2},a_{3},a_{4},a_{5}\right\}$$, then the number of one one function so that $$f(x_{i})\neq x_{i},x_{i}\ \in\ A$$ is

If $$f(x)=x-\cfrac{1}{x}$$ then number of solutions of $$f(f(f(x)))=1$$ is