Can an invertible function have more than one x-intercept?

No.

If the function has more than one x-intercept then there are more than one values of x for which y = 0. This means that, for the inverse function, y = 0 should be mapped onto more than one x values. That is, the inverse function would be many-to-one.

But a function cannot be many-to-one. So the "inverse" is not a function. And tat means the original function is not invertible.