Functions

y is a function of x, that is, y = f(x), means that for a value of x, there is ONLY ONE value of y to be calculated. That is, you cannot get more than one value of y, ALSO, you cannot get no value of y.

For (a), when you are given a value of x, you can calculate ONE and ONLY ONE value of y, which is 2*x, therefore, y is a function of x.

For (d), y = √(3x+1), for all the value of x ≥ 0 (actually for x ≥ -1/3 is also ok), you can get ONE and ONLY ONE y, so y is a function of x.

For (b), y² = 3x + 4, you can check that when x = 0, y can be solved to be either 2 or -2, therefore, you cannot get EXACTLY ONE value of y, so y is not a function of x.

For (c), y = √(2x-1), you can see that when x = 0 (or any value less than 1/2), you cannot calculate a real value of y, so y is NOT a function of x.

這個寫法 : y = √(3x+1) 代表正根，即 y 只取 > 0 的值。所以只有一個數值。例如

y = √9 ; y = +3

但 y² = 9

則 y = +3 或 y = -3。可以有两個數而並非單值。

如果

y = -√9 ; y = -3

2013-11-18 19:14:45 補充：
更正：
這個寫法 : y = √(3x+1) 代表正根，即 y 只取 > 0 或 = 0 的值。