If f(x)=`{[1,;x >0],[0,;x=0],[-1,; x<0]:}` then f is continuous or not

If 0ltalt1 and f is defined as f(x)={[x^(a),x>0],[0,x=0]} ,then which of the following is true.

Let f: R->R be the signum function defined as f(x)={1,\ x >0,\ \ \ \ 0,\ x=0,\ \ \ \ \-1,\ x R be the greatest integer function given by g(x)=[x] . Then, prove that fog and gof coincide in [-1,\ 0) .

Let g(x)=1=x-[x] and f(x)={-1, x < 0 , 0, x=0 and 1, x > 0, then for all x, f(g(x)) is equal to (i) x (ii) 1 (iii) f(x) (iv) g(x)

If f(x)={{:(|x|+1,xlt0),(0,x=0) ,(|x|-1,xgt0):} for what value (s) of a does lim_(xrarra) f(x) exists?

If f(x)={{:(-1, x lt 0),(0, x=0 and g(x)=x(1-x^(2))", then"),(1, x gt 0):}

Let g(x)=1+x-[x] and f(x)={(-1",",x lt 0),(0",",x=0),(1",",x gt 0):} , then for all x, f[g(x)] is equal to

Let g(x)=1+x-[x] "and " f(x)={{:(-1","x lt 0),(0","x=0),(1","x gt 0):} Then, for all x, find f(g(x)).

If f(x)={{:(,|x|+1, x lt 0),(, 0,x=0),(,|x|-1, x gt 0):}" then "underset(x to a)lim f(x) exists for all

Let g(x)=1+x-[x] and f(x)={{:(-1",", x lt 0),(0",",x=0),(1",", x gt 0):} , then for all x , f[g(x)] is equal to