MATH: which one of these is a one to one function ?

Question

1. y = x^2 - 5

2. y = x^4 + x^2 + 1

3. y = 3x + 4

4. x^2 + y^2 = 9

i got the answer # 4..is that correct ?

Answer 1

No. It is 3. Every other answer can have both a positive and a negative number as a solution so it is not one to one.

Answer 2

3

Answer 3

pick a y, solve for x (to see if it's even a function, pick an x, solve for y, and if y is unique, it is)

1. let y = 11. then 16 = x², x = ±4, so not 1 to 1

2. generally, even functions like 1, 2, and 4 are not 1 to 1, since f(x) = f(-x), so f inverse of f(x) will not be unique. so see this one as

y = (x² + 1)²

so if y = 25, x² + 1 = ±5, and if x² + 1 = 5, x² = 4, x = ±2

4. see that x² ? so if y = 2, x² + 4 = 9,
x² = 5, x = ±√5. inverse is not a function.

3. the only odd function up there is y = 3x + 4, so x = (y-4)/3 is its inverse.
This function is 1 to 1.

Answer 4

I don't understand all the answers that say 3 is 1 to 1. It seems more like 3 to 1. Y has to increase by 3 for every X increase of 1. Isn't that 3 to 1? Why are people saying it's 1 to 1?

Answer 5

"one -to-one" function refers to a functionwhere you obtain a certain value for exactly one value of the variable. It does not matter what the value is or at what rate it changes. With number 4 you obtain the same number y if you replace x by -x. Moreover, this does not even represent a function, since for a given value of x, you can get both y and -y (not only one value, as required by the definition of a function)

Also, note that 3 is not an odd function as stated by the previous answer, since if you replace x by -x, the result is not -y: y(-1)=1, y(1)=7

Answer 6

Nope. You're looking for a 1st order function. Try again. Hint: Contains a 4.

Answer 7

well i was gonna say 3, but u confused me

Answer 8

3 i think.

Answer 9

You're right.