Question

Calculate the following:

a) Find g(f(1))
b) Find lim x-> 1+ g(f(x))
c) Find f(g(0))
d) Find lim x->0- f(g(x))

f(x)= 1-x, x<1
1, x=1
x-1, x>1

g(x)= -x, x<0
2, x=0
x+2, x>0

This is where it gets hard. I have a graph for f(x) and one for g(x). I will explain them. The graph for f(x)has an open circle at 1 on the x-axis and a line extending straight out from it going to the right. Another line extends out from it as well in the left direction and passes through (0,1). A closed circle is located at (1,1).

The graph for g(x) has an open circle at the origin with a line extending from it going left. A closed circle is located at (0,2) with a line extending from it going to the right.

I have been struggling with these and I am now also confused as to why he included the info with the x is <,=,> part, as I have never seen this before. Could someone please help. I would really appreciate it.