one to one funcitons?

Question

can anyone clarify with me whether or not the following functions are one to one or not
f(x)=x-1 i said yes
f(x)=x^2+1 no
f(x)=x^3 yes
f(x)=n/2 no

i meant x-2 sorry

Answer 1

I agree with all your answers except MAYBE the last one...why don't the variables match?

Shouldn't it be f(x) = x/2?

If so, then it would be the same as f(x) = 1/2 x, which is linear, which is definitely 1-to-1.

If you REALLY mean f(x) = n/2, where n is some other number, then you'd have a horizontal line at y = n/2, which is not 1-to-1, so you'd be right.

As you've probably noticed, even powers of x are not 1-to-1. Odd powers are.

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f(x) = x - 2 is also linear and one-to-one.

Also, vacaloco thumbs-downed us all so his answer would appear to be better.

Answer 2

All those seem to be correct. You can check by graphing the relations. You can check it by using the vertical and horizontal line tests. The horizontal line test tells you if a function is one-to-one.The horizontal lines you draw through the function must only intersect at one point.

Note: If a relation doesn't pass the vertical line test, then it is not a
function and will not have a one-to-one relationship.

Answer 3

One to one means that for any given value of x, there is only one value of f(x). In these cases:

f(x) = x - 1, for any x there is only one f(x)

f(x) = x^2 + 1, for a value of x and for the negative of that value the f(x) is the same because when you square a negative you get a positive.

f(x) = x^3, due to taking x to the power of three you once again get a unique f(x) for any given x (negative x gives a negative and positive x gives a positive answer)

f(x) = n/2, this is not a function of x - there is no x in the equation.

Answer 4

f(x) is 1-1 if, f(x)=f(y) => x=y

f(x)=x-1 i said yes
since, x-1=y-1 => x=y
f(x)=x^2+1 no
f(1) = 3 = f( -1)
f(x)=x^3 yes
x^3 = y^3 => (by taking cube root) x=y
f(x)=x-2 yes
x-2 = y-2 => x=y .