proove it,
2007-01-19 08:06:24 · 7 answers · asked by Anonymous in Science & Mathematics ➔ Mathematics
A function is 1:1 means that
f(x1) = f(x2) iff x1 = x2
Since you have a square in this function, it's not 1:1, because any positive number has two square roots.
This generates an infinite set of pairs of numbers (x1 and x2) where x1 is not equal to x2 but f(x1) = f(x2)
You can see this if you graph the function. Such pairs would show up as places on the curve where a horizontal line crosses more than once. This is the meaning of the "horizontal line test" for 1;1 functions. This function graphs as a parabola, which is symetric to its vertical axis, and so every point (except the vertex) has its counterpart where the 1:1 criteria is violated.
(edited later)
I see a few people are confused about this so I looked it up...
http://www.mathwords.com/h/horizontal_line_test.htm
The vertical line test is to tell if a relation is a function, that is, to tell if each x generates no more than 1 y. If the same x generates two different y's that shows up as a violation of the vertical line test, and the relation is not a function.
A parabola such as the one you cited is a function, as you said it is. However, your question is not whether it is a function but whether it is 1:1, and be assured that it isn't.
The horizontal line test is to tell if a function is 1:1, that is, to tell if each y comes from no more than 1 x. If the same y can come from two different x's, this shows up as a violation of the horizontal line test, and shows that, while the relation is a function, it is not invertible unless you restrict the domain. This is why the relation y = +/- sqrt x (a parabola lying on its side) is not a function but y = sqrt x, (understood to mean principle or positive square root) is a function, it looks like half a parabola lying on its side.
2007-01-19 08:23:23 · answer #1 · answered by Joni DaNerd 6 · 0⤊ 0⤋
No, it is not a one-to-one function (that is, it is not invertible, doesn't have an inverse, cannot pass the horizontal line test in which a horizontal line passes through its graph at no more than one point).
y=-x^2+4x+1 is the expression rewritten.
If you take the - sign off the x^2, it is (-1) x^2 +4x +1.
You still basically have a quadratic expression which graphs a parabola. A parabola can never pass the horizontal line test. Any horizontal line passes through a parabola twice.
2007-01-19 08:55:55 · answer #2 · answered by kathyw 7 · 1⤊ 0⤋
Indeed, a function that is!
The equation you gave is second order and is a quadratic so 'tis therefore a parabola, and therefore a function! As the fizixx said, use the vertical line test. If it passes (and it does), then it is a function.
As a sidenote - you only use the horizontal line test to check if the inverse of a function is a function.
2007-01-19 08:49:37 · answer #3 · answered by emsviper 2 · 1⤊ 1⤋
no if y=1 then we have 4x-x^2=0 then x=0 and x=4
(0,1) and (4,1) is in this function
2007-01-19 08:13:28 · answer #4 · answered by Esmaeil H 2 · 0⤊ 0⤋
The function you gave IS a one-to-one function.
It has to pass the vertical line test....which it does. The other is a pitfall which easily fooled these other folks doesn't apply here.
2007-01-19 08:33:37 · answer #5 · answered by Anonymous · 0⤊ 1⤋
ofcourse not.b"cause f(3)=f(1)=4
2007-01-19 08:13:26 · answer #6 · answered by Lady 2 · 0⤊ 0⤋
Yes. That is exactly how you would do it. Try it now, before you look at any of the other answers.
2016-05-23 22:20:43 · answer #7 · answered by ? 4 · 0⤊ 0⤋