Question AoPS Intro to Algebra chapter 16 (functions)

[Sebastian (a lady)]

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?

[nmoira]

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.

[Sebastian (a lady)]

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

[Sebastian (a lady)]

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.

[regentrude]

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

[Jane in NC]

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.

[Sebastian (a lady)]

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

[Sebastian (a lady)]

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?

[Jane in NC]

 

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.