(9) If `f(x)=|x|` ,show that `f'(2)=+-1` .

If f(x)=|x| then show that f'(3) =1

If A=[(1 ,2 ),(2, 1)] and f(x)=x^2-2x-3 , show that f(A)=O .

If f(x)=1/(1-x) , show that f[f{f(x)}]=xdot

If f(x)=x^3-1/(x^3) , show that f(x)+f(1/x)=0.

If f(x)=(x+1)/(x-1) , show that f{f(x)}=xdot

f:R-{0} to R is defined as f(x)=x+1/x then show that (f(x))^(2)=f(x^(2))+f(1)

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

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

Let f defined on [0, 1] be twice differentiable such that |f " (x)| <=1 for x in [0,1] ,if f(0)=f(1) then show that |f'(x)|<1 for all x in [0,1] .

Let f be a real function defined by f(x)=sqrt(x-1) . Find (fofof)(x)dot Also, show that fof!=f^2 .