Sebastian (a lady) Posted March 25, 2013 Share Posted March 25, 2013 Lesson 16.2 is on combining functions. Sample problem 16.9 uses f(x)=square root of x and g(x)=square root of (x^2 -x-9) I'm confused as to how square root of x would be a function. Aren't there two possible outputs to any given input (even fit you restrict x to numbers greater than or equal to zero). What am I missing here? Quote Link to comment Share on other sites More sharing options...
nmoira Posted March 25, 2013 Share Posted March 25, 2013 Lesson 16.2 is on combining functions. Sample problem 16.9 uses f(x)=square root of x and g(x)=square root of (x^2 -x-9) I'm confused as to how square root of x would be a function. Aren't there two possible outputs to any given input (even fit you restrict x to numbers greater than or equal to zero). What am I missing here? If it's under a radical sign, it's the positive square root only. Quote Link to comment Share on other sites More sharing options...
Sebastian (a lady) Posted March 25, 2013 Author Share Posted March 25, 2013 Really? Hmm. I guess that's what I get for sw Quote Link to comment Share on other sites More sharing options...
Sebastian (a lady) Posted March 25, 2013 Author Share Posted March 25, 2013 Really? Hmm. I guess that's what I get for switching between aops and Dolciani. I don't recall the Dolciani book making that distinction. Quote Link to comment Share on other sites More sharing options...
regentrude Posted March 25, 2013 Share Posted March 25, 2013 The definition of the function "square root of x" is the non-negative number whose square is equal to x. Quote Link to comment Share on other sites More sharing options...
Jane in NC Posted March 25, 2013 Share Posted March 25, 2013 Really? Hmm. I guess that's what I get for switching between aops and Dolciani. I don't recall the Dolciani book making that distinction. Yes it does. If you take the square root of x^2, you have to account for the fact that x could be positive or negative. But sqrt(x) yields a non-negative result. Quote Link to comment Share on other sites More sharing options...
Sebastian (a lady) Posted March 25, 2013 Author Share Posted March 25, 2013 Ah I see now that section 1.8 on page 42 states this assumption. (That was a long time ago.) Quote Link to comment Share on other sites More sharing options...
Sebastian (a lady) Posted March 25, 2013 Author Share Posted March 25, 2013 Yes it does. If you take the square root of x^2, you have to account for the fact that x could be positive or negative. But sqrt(x) yields a non-negative result. So sqrt(9) = 3 but if I have x^2=9 and I take the sqrt of both sides, I get x= +3 or -3 Is that the correct distinction? Quote Link to comment Share on other sites More sharing options...
Jane in NC Posted March 25, 2013 Share Posted March 25, 2013 So sqrt(9) = 3 but if I have x^2=9 and I take the sqrt of both sides, I get x= +3 or -3 Is that the correct distinction? Yup. Quote Link to comment Share on other sites More sharing options...
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