The difficult thing about inventing a new religion is that you have to explain why it is new. With Mormonism, the answer to this is apostasy. Specifically, the "Great Apostasy". Apparently, not long after the Apostles died (except John, whom Doctrine and Covenants 7:1-3 claims is still alive), the true Gospel perished from the Earth, and Christianity divided into countless false denominations. Joseph Smith was eventually selected to restore the true faith to the Earth.
Now, as a Christian, I of course believe the true Gospel has been followed by false gospels. False teachers, and what Jesus describes as "wolves in sheep's clothing", didn't even wait for Jesus to ascend into Heaven before creeping around the Earth stealing souls for Satan. Of course there are false denominations, many of which have existed for 2,000 years, and yes, some arose shortly after the Apostles died.
However, the existence of false gospels does not mean the true gospel had been lost. It just means that, since there is only one truth, and countless lies, it appears that way sometimes. But of course, God's word didn't disappear. What we can actually do, then, is look through history and compare the beliefs of groups and individuals to ask whether or not the Church survived. As it turns out, not only did the Church survive throughout the ages, it flourished. The very nation in which Joseph Smith was born was founded by men whose personal religious views drew very heavily from the word of God. So we see from scripture that the Great Apostasy couldn't happen (Matthew 16:18), and from history that it simply didn't.
But let's imagine it did. Let's pretend that God sent His own Son, who raised up 12 Apostles (and promised one of them he wouldn't die until He returned, for the very purpose of bringing souls to Christ), and yet still failed to preserve the Gospel for more than a century. If God is so weak that He allegedly failed to preserve the Gospel for just 100 years back then, imagine how quickly a similar Great Apostasy could happen now.
As it turns out, the Mormonism of today is not the same as the Mormonism of Joseph Smith's day. In fact, in spite of Joseph Smith originally claiming the Book of Mormon is "the most correct book", there have been literally thousands of alterations to it. Since Mormonism obviously is not the same religion as it was in the time of Joseph Smith, is it not possible that there was another "Great Apostasy"? Using the logic of the Mormon Church, yes, it absolutely is. Using the logic of the Bible, it is impossible for there to have been another great apostasy, as there was never a first great apostasy. There are, therefore, two possibilities:
1. The Bible is false, therefore Mormonism is false because it affirms the Bible.
2. The Bible is true, therefore Mormonism is false, because it conflicts with the Bible.
Mormonism is false, Mormons are committing blasphemy, Mormons need to repent and be saved. Not "after all we can do", as the Book of Mormon says, but after all Christ has done.