No, Duet Display is not free.
According to their site, Duet Display offers two pricing plans for regular consumers. Their basic option, "Duet Display" is a one-time purchase of $9.99. This plan allows you to use your iPad as a wired display with basic touch control. Their more premium option, "Duet Air" is an annual subscription of $19.99. This plan has more bells and whistles, incuding improved performance, pixel perfect rendering, advanced gesture control, and the ability to use your Mac or PC as a second display. Finally, there is an Enterprise plan with custom pricing for larger organizations that can benefit from bulk pricing.
Mentioned in this answer
Duet Display
Use your iPad as a second display for your Mac