# Question AoPS Intro to Algebra chapter 16 (functions)

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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?

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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.

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Really? Hmm. I guess that's what I get for sw

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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.

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The definition of the function "square root of x" is the non-negative number whose square is equal to x.

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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.

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Ah I see now that section 1.8 on page 42 states this assumption. (That was a long time ago.)

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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?

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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.

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