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Determine whether or not the function determined by the given equation is one-to-one.$$f(x)=2 x^{2}-7$$

No

Algebra

Chapter 4

Exponential and Logarithmic Functions

Section 1

Inverse Functions

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Lectures

01:02

Determine whether or not t…

00:23

Determine whether the func…

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00:59

Decide whether each functi…

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So if we want to determine if this is 11 tau one or not, what we need to do is plug in some arbitrary values A and B, and then see if a and B must be equal to each other. Um, in this case is we have a quadratic. We know the shape of a quadratic is like a you, so it would fell the horizontal line test. So what you could do is really just find two values where they are different, but they have the same output. Eso just kind of often the side. All right, this But I'll do it more rigorous is Well, um, because we could essentially just do like f of negative one. And when we plug f of negative one in. So that would be, uh, one times two minus seven, which would be negative five. And then notice F one is also equal to negative five. So these two are equal to each other, but negative one is not equal toe one. And just from this, this implies ffx is not want one. So you could just do that. I mean, this is essentially what you would normally do. You just need to come up with one counter example. But if you have a hard time trying to find this, I'll show you another way how you may be able to come to the same conclusion as well. Um, so let's just go ahead and plug in A and B. We have f of A is equal to F A B, so that would give us two X squared minus seven is equal to hope not to x to a squared to a squared minus seven is equal to two B squared minus seven. So if we subtract seven and then divide by two on each side Um, notice we didn't know what a squared is it to be squared. And so now, at this point, if we were to take the square root on each side, then this is going to give a is equal to plus or minus B. So this here contradicts the fact that a should be equal to be because we can have where a is B or negative B. And so this is another way you can go ahead and say Okay, which implies AP of X is not 1 to 1. So either of these ways is a sufficient way to show it. It just kind of depends on which way you think is the better way. So I guess I should say like way one and then over here this is way too. But I mean, normally, if you confined to numbers way one is the better way to go about doing it.

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