The red curve is the graph of a function because it passes 
the vertical line test.  That is, there are no places where 
a vertical line crosses the graph more than once.

It does not have an inverse because it does not pass the
horizontal line test, as we can see because the green
horizontal line crosses the curve in two points.

It has f(1) > 0 since the y-coordinate is 12 where x=1, and
12 is certainly greater than 0.

f(x) > x  at all values of x because it is always above the 
blue line, whose equation is y = x.

Edwin