SOLUTION: I am still unsure when it comes to functions. I have a question that is as follows: Is f(x) = x^2 + 2x - 3 a one-to-one function? Explain your answer.
When figuring out the p
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Question 213488: I am still unsure when it comes to functions. I have a question that is as follows: Is f(x) = x^2 + 2x - 3 a one-to-one function? Explain your answer.
When figuring out the problem if f(a) = f(b) then my answer would be no as
a^2 + 2a - 3 = b^2 + 2b -3 does not factor down to a = b.
Am I figuring this correctly?
Thank you = Lori
Found 2 solutions by Theo, jim_thompson5910:
Answer by Theo(13342) (Show Source): You can put this solution on YOUR website!
if every value of x yield one and only one value of y, the equation is a function.
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f(x) = x^2 + 2x - 3 is a function.
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let y = f(x) and we can graph this equation.
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if f(a) equals f(b), this does not mean the equation is not a function.
you would have one value of y for 2 values of x.
f(x1) would be y
f(x2) would be y
you still only have one value of y for each value of x so the equation is still a function.
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the definition of a function is one value of f(x) for each value of x.
f(a) = f(b) does not violate this.
take y = x^2
let a = 2
then f(a) = 4
let b = -2
then f(b) = 4
f(2) = f(-2)
you have f(a) = f(b) but you still only have one value of y for each value of x.
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Answer by jim_thompson5910(35256) (Show Source): You can put this solution on YOUR website!
You're on the right track. A function is one-to-one if only means . In other words, if two outputs of a function are equal, then the inputs must be equal for the function to be one-to-one.
So if you think that this function is NOT one-to-one, then simply pick a counter-example to prove this claim false. Let's say that . Plugging this into gets us . Now solve for 'x' to get or
So if we plug in either 0 or -2 into f(x), we'll get -3 as an output. Ie. . Since , this means that the function is NOT one-to-one. So you are correct.
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