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Which equation defines a one-to-one function? Explain why the others are not, using specific examples.A. $f(x)=x$B. $f(x)=x^{2}$ C. $f(x)=|x|$D. $f(x)=-x^{2}+2 x-1$
a. $$ f(x)=x $$
Algebra
Chapter 12
Inverse, Exponential, and Logarithmic Functions
Section 1
Inverse Functions
Functions
Exponential and Logarithmic Functions
Campbell University
McMaster University
Baylor University
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Okay, so we want to see which of those four functions is 1 to 1. The way that we're going to sell This ends by graphing. So let's start with f of X is equal to X because I was practically wise. He called the X, which is just our diagonal line. You know, we have X squared, which is our parabola, the absolute value of X, which looks like a bee. And then we have There's big equation right here. But if you notice we have a square, so that is also going to be a parappa. Okay, now the way that we're going to see if it's wanted one, we're going to use the horse onto line test. So if the horse on the line on Lee crosses the function ones, that is 1 to 1. So, like, this one on the cross is right here. So this would be 1 to 1. Now, this crosses at two points. So it is not wanting one same thing with this one. And the same thing with this one Okay, isn't not wanting one into the only one that is want you wanted f of x f of X is equal to x and so that I there's going to be our answer
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