How can methane absorb infrared light within wide range of frequency but CO2 can't?
Comparing the vibrational spectra of two different molecules is just like wondering why two people do not have the same fingerprints. The simplest answer is that these two molecules are different molecules with different atoms hence their vibration modes are supposed to be different.

IR Spectra of Methane and Carbon dioxide are available in NIST. This is how real spectroscopy looked like before the focus shifted from true science to fancier presentations and instruments became black-boxes. Anyway, all you have to note both methane and carbon dioxide absorb quite strongly in the typical range of infrared light 400 to 3800 $cm^{-1}$. The question of wide range does not arise as you can see from the spectra, their absorption band positions are different. Methane's spectra is more complex just because it has more active vibrations (dipole moment change is non-zero) and one can see the fine rotational structure of methane but carbon's dioxide's rotational lines are not resolved.