Making use of take on and take up is often baffling. Here’s something that can help you decide next time you use either of the two:
‘Take on‘ is to undertake some work ( Is he ready to take on his new responsibilities ?) or to accept as a challenge ( I’m ready to take on that bully.)
‘Take up‘ is to occupy oneself with some work ( She took up painting in her spare time.) or simply to occupy ( This dining table would take up half of our living room.)
Hope this differentiation helps you make your choice of phrase easier in future.
( Ref. Webster’s Unabridged Dictionary)