Contemporary philosophers of religion have predominantly focused on understanding the nature of faith, yet there has been a lack of attention towards a particular type of faith that we can call inquiry-based faith. This paper aims to address this gap by exploring some challenges associated with inquiry-based faith. I argue, in particular, that while this is a widespread kind of faith, we face a dilemma in showing how it is possible and plausible. On the one hand, faith that P requires acceptance of P, and on the other, if someone is inquiring into whether P is the case, she must not already accept that P is the case. Borrowing a conceptual framework from recent literature on inquiry, I propose a solution to this dilemma by appealing to parts of the story of Abraham in the Quran. I suggest, specifically, that one can have faith that a partial answer to a question is the case, and at the same time, seek further inquiry into the question for a more complete answer. As such, I support the idea that inquiry-based faith is a possible and plausible option for both faithful people and inquirers.