唔識做功課25

Question
2y² = x (x ≥ 0)
Determine whether y is a function of x where x and y are real numbers.

Solution
2y² = x
y² = x/2
y = ±√(x/2)

For some (actually each this time) value of x, there are more than one corresponding value of y, therefore, y is NOT a function of x.

Example
Let x = 50
2y² = x
2y² = 50
y² = 25
y = 5 or -5 (there are two values possible)

Teaching
同學問：「有啲混亂,都唔知假設x係幾多至好」

那怎麼 let 才方便我們思考和計算呢？

先想想
2y² = x 可變成 y² = x/2

如果 x/2 是一個 perfect square (完全平方)，那就好辦事了。

若 x/2 = 1² = 1 即 x = 2
若 x/2 = 2² = 4 即 x = 8
若 x/2 = 3² = 9 即 x = 18
若 x/2 = 4² = 16 即 x = 32
若 x/2 = 5² = 25 即 x = 50

本部分旨在教你如何思考可以順暢一點。

如果你夾硬隨意寫個數，其實也可以。
例如，x = 24.86
2y² = 24.86
y² = 12.43
y = ±√12.43 (also two different values)