Relations and F...

For $$a,\ b\ \epsilon \ R-\left\{ 0 \right\}$$, let $$f(x)=ax^{2}+bx+a$$ satisfies $$f\left(x+\dfrac{7}{4}\right)=f\left(\dfrac{7}{4}-x\right) \forall \ x\ \epsilon\ R$$.
Also the equation $$f(x)=7x+a$$ has only one real distinct solution.
The value of $$(a+b)$$ is equal to

$$f(x)$$ is a cubic polynomial with it's leading coefficient 'a'. $$x=1$$ is a point of extremum of $$f(x)$$ and $$x=2$$ is a point of extremum of $$f(x)$$. Then?

If x is real, then $$\dfrac{x^2+2x+c}{x^2+4x+3c}$$ can take all real values if?

If $$\dfrac{{{x^2} + {y^2}}}{{x + y}} = 4$$, then all possible values of $$(x-y)$$ is given by 

The area of the region $$R = \{(x, y) : |x| \le |y| \, \text{and} \, x^2 + y^2 \le 1 \}$$ is 

Let $$R = \left \{(1, 3), (4, 2), (2, 4), (2, 3), (3, 2)\right \}$$ be a relation on the set $$A = \left \{1, 2, 3, 4\right \}$$. The relation $$R$$ is

If  $$f:R\rightarrow R,g:R\rightarrow R$$ are defined by $$f(x)=5x-3,g(x)={ x }^{ 2 }+3,$$ then $$(go{ f }^{ -1 })(3)=\\ $$

$$f:c \to c$$ is defined as $$f(x) = \dfrac{{ax + b}}{{cx + d}},bd \ne 0$$ then $$f$$ is a constant function when,

If $$f$$ is a real valued function such the $$\left| {f\left( x \right) - f\left( y \right)} \right| \le {\left| {x - y} \right|^3}$$ then $$f'\left( x \right)$$

Let for $$a\ne a_1 \ne 0$$,   $$f(x)=ax^2+bx+c$$, $$\,\,\ g(x)=a_1x^2+b_1x+c_1$$ and $$p(x)=f(x)-g(x)$$. If $$p(x)=0$$ only for $$x=-1$$ and $$p(-2)=2$$, then the value of $$p(2)$$ is :