These three diagrams illustrate the root position (1 3 5), first inversion (3 5 1), and second inversion (5 1 3) of the F chord.
This example shows the root position, first inversion, second inversion, and an octave of the root position of the F chord.
One of the reasons inversions are so useful is that they enable you to find chord shapes which are close together on the keyboard. Here the C chord appears in root position, the F chord is in second inversion and the G chord is in first inversion. The left hand plays the root note of each chord. When you play chord voicings which are close together on the keyboard, the chord changes sound smoother and often contain common tones, e.g., the chords C and F both contain the note C. Always try to find smooth connections between chords.
Here are some examples showing typical uses of these inversions. Notice how much easier the chord changes are. By using inversions which are close together, it leaves you free to concentrate on other important things such as rhythm.
Here is a 12 Bar Blues making use of the same inversions. Notice the emphasis on rhythm in this example, as well as the interplay with the other instruments.