Relations and F...

If f(x)=ax+b, where a and b are integers, f(-1)=-5 and f(3)=3, then a and b are equal to

Let 'f' be a function defined from $$R^{+}\rightarrow R^{+}$$  .If $$(f(xy))^{2}=x(f(y))^{2}$$ for all positive numbers x and y . If f(2)=6, find f(50)=

Let $$R = \left \{(2, 3), (3, 3), (2, 2), (5, 5), (2, 4), (4, 4), (4, 3)\right \}$$ be a relation on the set $$\left \{2, 3, 4, 5\right \}$$, then

If  $$g(f(x))= |sinx|$$  and  $$g(f(x))= sin^2 \sqrt{x},$$  then

Let $$f(x)=\left | x-x_{1} \right |+\left | x-x_{2} \right |$$ where $$x_{1} and x_{2}$$ are distinct  real numbers. Then the number of points at which f(x) is minimum is:

If $$f(x)=\frac{1}{\sqrt{x+2\sqrt{2x-4}}}+\frac{1}{\sqrt{x-2\sqrt{2z-4}}}$$  for  x > 2 then f(11) = 

If $$\displaystyle f(x)= \dfrac{7^{1+\ln x}}{x^{\ln 7}}$$  then $$f (2015) $$ is equal to

If $$f(x)=x+x^{2}$$ is expanded as a Fourier series in $$(-\pi ,\pi )$$, then $$a_{0}$$=

If $$(x^{2}-2)+(y+3)i=7+4i$$  then x and y are 

If $$f\left(x+\dfrac{1}{x}\right)=x^2+\dfrac{1}{x^2}$$ then $$f(x)=?$$