Relations and F...

If $$f(x)=\quad cos(\log { \quad x } )$$, then
$$f({ x }^{ 2 })f({ y }^{ 2 }) -\frac { 1 }{ 2 } \left[ f(\frac { { x }^{ 2 } }{ 2 } )+f(\frac { { x }^{ 2 } }{ { y }^{ 2 } } ) \right] $$ has the value :

If $$f\left( x+\frac { 1 }{ 2 }  \right) +f\left( x-\frac { 1 }{ 2 }  \right) =f\left( x \right) ,\quad \forall x\in \quad R$$, then $$f\left( x-3 \right) +f\left( x+3 \right)$$ is equal to 

$$f(x) = \frac{{1 - x}}{{1 + x}}$$ for $$x \ne  - 1$$ then $$f(x) + \left( {\frac{1}{x}} \right)$$ is $$(for\,\,x \ne 0)$$

Let $$A$$ be set of first ten natural numbers and $$R$$ be a relation on $$A$$ defined by (x , y) $$\in$$ $$R$$ $$\Rightarrow$$ x + 2y = 10 , then domain of $$R$$ is

If  $$f(x)=x^2-5x+6$$, find $$f(A)$$ if $$A=\begin{bmatrix} 2 & 0 & 1 \\ 2 & 1 & 3 \\ 1 & -1 & 0 \end{bmatrix}$$.

If $$ f ( x ) = x ^ { 3 } + x ^ { 2 } f ^ { \prime } ( 1 ) + x f ^ { \prime \prime } ( 2 ) + f ^ { \prime \prime \prime } ( 3 ) . $$ Then $$ f ( 2 ) $$ is

If f(x) =$$\dfrac{1 - x}{1 + x} , then f [f (cos 2\theta)] =$$

If f (x) = $$\dfrac{x -|x|}{|x|}, then f (-1) = $$

If $$f\left( x \right) ={ x }^{ n }$$, then the value of $$f(1)-\dfrac { f'\left( 1 \right)  }{ 1! } +\dfrac { f''\left( 1 \right)  }{ 2! } -\dfrac { f'''\left( 1 \right)  }{ 3! } +...+\dfrac { \left( -1 \right) ^{ n }{ f }^{ n }\left( 1 \right)  }{ n! } $$ is 

Let $$F(x)$$ be the primitive of $$\cfrac{3x+2}{\sqrt{x-9}}$$ with respect $$'x'$$. If $$F(10)=60$$. Then the sum of digits of the value of $$F(13)$$ is