If `f(x)=(2x+1)/(3x-2)=y`,show that x=f(y).

If f(x)=(x-1)/(x+1) ,then show that f(-1/x)=-1/f(x) .

If f(x)=(x-1)/(x+1) ,then show that f(1/x)=-f(x) .

If y=sqrt(x)+(1)/sqrt(x) , then show that 2x(dy)/(dx)+y=2sqrt(x) .

If f(x)=(5x+3)/(4x-5) , (x ne 5/4) show that f{f(x)} is a identity function.

If f : [-1,1] rarr R, f(x)=x/(x+2) , show that f is one-one and find the inverseof f : [-1,1] rarr range of f.

If f (2) = 4 andf'(2) = 1, show that lim_(xrarr2)(xf(2)-2f(x))/(x-2)=2

If f : R rarr R be defined by f(x)=2x-3 and g : R rarr R be defined by g(x)= (x+3)/2 , show that fog=gof=I_R

Let f:R rarr R is defined by f(x)=3x-2 and g:R rarr R is defined by g(x)=(x+2)/3 . Show that f.g=g.f .