Question

Which element is oxidized and which element is reduced in this redox reaction?

CO2(g) + H2(g) --> 2CO2(g) + H2O(g)

Is Oxygen oxidized and hydrogen reduced?

Answer 1

No. Oxidation is the loss of electrons; reduction is the gain of electrons. Your equation is not right to begin with. It shows a reduction half but NOT an exidation half. I suspect you intended to write
CO2(s) + H2(g) ==> CO(g) + H2O(g)

Start by assigning oxidations numbers to each. From the left:
C = 4; O - -2 each; H = 0.
On the right we have
C = +2; O = -2; H = +1 each; O = -2.

Now you look to see what has changed.
C has changed from +4 each to +2 each which means a gain of electrons.
H has changed from 0 on the left to +1 each on the right which is a loss of electrons.