Which of the following are one-to-one functions?

Question

A. f(x) = + x
B. f(x) = x(1/3)
C. f(x) = -x
D. y = x(1/2)
E. y = ln(x)
F. y = | x | + 2

I picked B, D, and E but I was wrong. Why?

Answer 1

B, D, and E are all one-to-one, but so are A and C. A function is one-to-one if for all possible a and b, f(a)=f(b) implies that a=b. In other words, there are no values of f(x) taken by more than one value of x. In case A), if f(a)=f(b), then by definition of f(x), a=b. The idea is exactly the same for C).

Answer 2

All are one-to-one except F. F does not pass the horizontal line test and has 2 elements in the domain that have the same value in the range.

All of the other functions have just on element in the range for each element in the domain.

Answer 3

A, B, C, and E are one-to-one functions.

By the way, A, doesn't really make much sense, since the + sign is not normally used as a unitary operator. But, it still holds as a one-to-one function.

Is D an exponent (^½) or a multiplication (* ½)? If it is a multiplication, then it is one-to-one. If it is an exponent, then it is not.

Not F.

Answer 4

A yes since given x you have one value of y
B also same reason as A
C also same reason as A
D No you can have negative and positive root
E No , there are no ln of negative number
C) No absolut value ox is the same for x and -x

Answer 5

All are one-one except 'F ' because in case of F for one value of x we will get 2 values of y. (Eg: y=|2|+2 =|-2| +2)

Answer 6

A C E F

Answer 7

C
E
F