If f(ax) = | a 1 0 ; ax a x² ; ax a x² | , using properties of determinants find the value of f(2x) - f(x).

f(ax) = | a 1 0 ; ax a x² ; ax a x² |

Therefore,
f(2x) = | 2 1 0 ; 2x 2x 4x² ; 2x 2x 4x² |
and
f(x) = | 1 1 0 ; x x x² ; x x x² |

f(2x) - f(x) = | 2 1 0 ; 2x 2x 4x² ; 2x 2x 4x² | - | 1 1 0 ; x x x² ; x x x² |

Expanding along row 1, we get:
| 2 1 0 ; 2x 2x 4x² ; 2x 2x 4x² | = 2(2x(4x²) - 2x(4x²)) - 1(2x(4x²) - 2x(4x²)) + 0 = 0
| 1 1 0 ; x x x² ; x x x² | = 1(x(x²) - x(x²)) - 1(x(x²) - x(x²)) + 0 = 0

Therefore, f(2x) - f(x) = 0 - 0 = 0