check the picture below.
if we run a vertical line test on that graph, like you see there, namely run vertical lines through it, we can see that one vertical line only hits the graph once, not twice or more.
on the vertical line test, if the graph is hit only once by each of the vertical lines, then the graph is a function.
We know, shortest distance between two points and
is :
So, distance between house and library is :
Distance between library and post office :
Distance between post office and house :
Therefore, minimum distance that you can ride your bike is (5.39+7.07+7) km = 19.46 km.
Hence, this is the required solution.