eric-said-that-if-fx2-x-and-gxx-2-then-fgx0-do-you-agree-with-eric-explain-why-or-why-not

Question

Eric said that if $f(x)=|2-x|$ and $g(x)=|x-2|,$ then $(f+g)(x)=0 .$ Do you agree with
Eric? Explain why or why not.

Finian Lickona · Accepted Answer

Okay, so in this question, we are given a function f of X equals the absolute value of two minus X. And we are told that Eric, the kids solving this question claims that this equation is the same as y equals two minus X when X is less than or equal to two. And why equals X minus two when X is greater than two? So we have to determine if Eric is correct or not. And the answer is yes, he is. So let&#x27;s take a sample value of X being less than to us. Let&#x27;s pick some number like one. For example, if we pick X as one, then we can rewrite this top equation right here is why equals two minus one, which is equal to one. And now, if we pick an X value greater than two, let&#x27;s say, three. We can rewrite this equation as y equals three minus two, which equals one. So if we plug this back into our original equation, we put one in for a value to minus one. Is one the absolute values one. And if we plug three in, we get two minus three, which is negative one in the absolute value of that is positive one. So this is correct

Heather Zimmers · Answer

here we have f of X, and we have G of X, and we want to know if they&#x27;re equal. So chances are what you&#x27;re going to do is look at f of X and realize that you can factor the numerator. You can factor in X out of both terms and you have X Times X minus one over X minus one and then you&#x27;re likely to think, Well, why don&#x27;t I just cancel the X minus ones? And then I&#x27;ll have left his ex and it&#x27;s just f of X equals X? Well, that&#x27;s only partially true. Go back to the original function and think about the domain. Let&#x27;s think about the domain of F of X. You can&#x27;t have zero for your denominator, so that means that X cannot be won. Let&#x27;s think about the domain of G of X G of X is just a polynomial function, and all real numbers can be and put it into their, and an output of real number will result. So the domain of G is all real numbers. So from that piece of information alone, we know that they&#x27;re not the same function. And if you want to consider the graph, consider the graph of G. It&#x27;s just going to be the line with a slope of one and a Y intercept of zero. So then how would the graph of F B any different? Well, since you can&#x27;t have X equals one, you can&#x27;t have the 10.11 that would be on G. And so you would have a whole at 11 And other than that, you would have something that looks like G. So these are not the same.

Nandini Singh · Answer

number two says that if F of axe equals X squared minus acts over X minus one and g about people&#x27;s acts, is it true that pickle juice the first thing you do is simple by half a box? How you can do that is on the topic in fact row. Yeah, X and then we get X minus one. Excellent. It&#x27;s one, and you can cancel. Excellent is on the top of the bottom. But whenever you do that you need displaced by the ex cannot equal one and then you&#x27;re left with just fax. So you can come to a conclusion that after sex equals g a box on the interval, I give her affinity told one non inclusive or one part of divinity. Reason being is GI effects exists on the domain of all real numbers. But effort backs exists on the domain of all real numbers except when X equals one. So you need to specify that because, uh, X equals one F of X will be undefined. Reggie of X will have a point. So at that point they will not be equal to each other, but all other points on the curve they will be equal to each other

Renée Przybyl · Answer

and this problem, we need to decide whether or not F of X is equal to G of X. We can do this by simplifying Methanex. You see there&#x27;s a common factor. X in the numerator, said X Times X minus one over X minus one. We could simplify that f of X is equal to X now this makes it seem that f of X is equal to G of X. But that is not the case because we have to go back to F of X and notice that the domain of F of X is going to be different because of the denominator. So X minus one cannot equal zero because it will make ffx under find. So that means X cannot equal one. Now the graph of F of X is going to look like this. And since X cannot equal one, there is going to be a hole in the line. Well, the domain of G of X is X can be anything from night of infinity to infinity and its graph is going to look like this. Now we see that these two graphs are different because there is no hole in G of X Well, there is a hole in f of X due to having the possibility of being undefined. So this means that G of X and ethics are different, so they&#x27;re not equal.

Shira Strong · Answer

Hi, everybody. We&#x27;re doing problem to now where it says that F of X is absolute value of X minus two and G of X is equal to the absolute value of X plus two. And the question is, we know that f of G of two f of G of two is equal to two and F A g 05 is equal to five. Andi f of G of seven is equal to seven on. We know the definition of inverse functions. Say that f of g of X. When you compose the functions with each other, you&#x27;ll get X. So the question is because when we plug in the value right, effigy of two means what we&#x27;re gonna pluck to into G an absolute value of two plus two is absolute value of four, which is for and then we would plug that into the F. And the absolute value of four minus two is absolute value to which is to sew these work. This works, this works and this works. The question is, if this is the definition of inverse functions, because these work are they automatically going to 80 inverse functions. Well, let&#x27;s try a different example. What if we pick a negative? What is f g of negative too? Well, let&#x27;s see what is G of negative too. We&#x27;re gonna plug and negative to into G. And we end up getting the absolute value of negative two plus two or the absolute value of zero, which is zero. Well, what&#x27;s f of zero? That would be the absolute value of zero minus two, which is the absolute value of negative too, which is equal to positive Thio. So what do we see here? When you plugged in a negative to you got a positive too. They&#x27;re not the same thing. So the answer is no. They are not in verse functions.

Problem

Give an example of a function g for which $2 \mat…

Problem 1 Easy Difficulty

Eric said that if $f(x)=|2-x|$ and $g(x)=|x-2|,$ then $(f+g)(x)=0 .$ Do you agree with
Eric? Explain why or why not.

Answer

No

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Algebra 2 and Trigonometry

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Absolute Value - Example 1

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