Which is not a function for all values of x?

Question

F(x)=x^3

F(x)=(-x)^1/2

F(x)=(-x)^1/3

F(x)=abs(-x)^1/2

F(x)=abs(-x)^1/3

Answer 1

In a function, for each x, there must be exactly one f(x). Not two, not three, not zero -- one means one!

Look carefully. Try plugging in 2 for x in each answer choice. Is there one for which you can't get ANY real value for f(x)?

Clues:

1. Absolute value bars turn things positive. e.g. |-2 - 3| = |-5| = 5.
2. Fractional exponents are roots! E.g. 8^2/3 = the cubed root of 8² = 4.
3. You can't take the square root of a negative number. (Well, you CAN, but your answer is an imaginary number, and that doesn't count!)

See video for more on functions, and the answer!