Domain of Radical Expression...2

[nycmathguy]

Section 2.7
Question 74

Set 49 - x^2 ≥ 0.

(7 - x) (7 + x) ≥ 0

7 - x ≥ 0

-x ≥ -7

x ≤ -7/-1

x ≤ 7

7 + x 0

x ≥ - 7

Domain: (-infinity, -7] U [7, infinity)

You say?

 

[MathLover1]

why did you set 49 - x^2 ≥ 0
if you have an expression and need to find a domain, you set it = to 0

49 - x^2 = 0

domain: R (all real numbers)

 

[nycmathguy]

why did you set 49 - x^2 ≥ 0
if you have an expression and need to find a domain, you set it = to 0

49 - x^2 = 0

domain: R (all real numbers)

Why did I set the radicand to be greater than or equal to 0?

1. Section 2.7 is all about polynomial inequalities.

2. Most You Tube tutors and teachers teach this to be the correct method.

Look here:

 

[MathLover1]

see this video:

 

[MathLover1]

wait a minute, I didn't realize you are that your 49 - x^2 is under square root

in that case you are right if you set 49 - x^2 ≥ 0

 

[nycmathguy]

wait a minute, I didn't realize you are that your 49 - x^2 is under square root

in that case you are right if you set 49 - x^2 ≥ 0

No problem. We all make mistakes.