anonymous
  • anonymous
If r(x) = 2 – x2 and w(x) = x – 2, what is the range of (w*r)(x)
Mathematics
  • Stacey Warren - Expert brainly.com
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SOLVED
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katieb
  • katieb
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SolomonZelman
  • SolomonZelman
is it ` (wº r)(x) `, or is it ` (w • r)(x) ` ?
anonymous
  • anonymous
the first one
SolomonZelman
  • SolomonZelman
Ok, you know that ` (wº r)(x) ` just means ` w(r(x)) ` in other words, you take the x in the function w(x), and plug in the function r(x) instead of it.

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SolomonZelman
  • SolomonZelman
w(x)=x-2 r(x)=2-x² ------------- so, you know that: w(\(\small\color{red}{x}\))=\(\small\color{red}{x}\)-2 and therefore: w(\(\small\color{red}{r(x)}\)) =(\(\small\color{red}{2-x^2}\))-2
SolomonZelman
  • SolomonZelman
can you simplify the w(r(x)) /
SolomonZelman
  • SolomonZelman
?
anonymous
  • anonymous
do you mean solve (w-x^2)-2?
anonymous
  • anonymous
2 instead of w
anonymous
  • anonymous
my bad
anonymous
  • anonymous
if so it would be -x^2
SolomonZelman
  • SolomonZelman
yes
SolomonZelman
  • SolomonZelman
so (wº r)(x) = -x² and you need to find the range of this
anonymous
  • anonymous
ok and how would i do that haha
SolomonZelman
  • SolomonZelman
x² \(\small \ge\) 0 (for any real number value of x)
SolomonZelman
  • SolomonZelman
so the range of x² is (0,+∞)
SolomonZelman
  • SolomonZelman
now, multiply both sides of: x² \(\small \ge\) 0 by -1, and you get
anonymous
  • anonymous
-x^2 and 0
SolomonZelman
  • SolomonZelman
and what is the sign, \(\small \ge\) or \(\small \le\)
anonymous
  • anonymous
<
SolomonZelman
  • SolomonZelman
-x² \(\small \le\) 0 like that?
anonymous
  • anonymous
yes
SolomonZelman
  • SolomonZelman
that is correct
anonymous
  • anonymous
yay ty
SolomonZelman
  • SolomonZelman
so -x² is at most 0, and can go into any very big negative values
anonymous
  • anonymous
mhm
SolomonZelman
  • SolomonZelman
so the range of -x² is?
SolomonZelman
  • SolomonZelman
well, it is at most 0, so we know that: ,0] and it can go into nagetive infinty so we know that: (-∞, 0]
anonymous
  • anonymous
thats it
SolomonZelman
  • SolomonZelman
yes
anonymous
  • anonymous
i just didnt know how to make a infinity sign haha
SolomonZelman
  • SolomonZelman
oh, 1. you click ALT, and hold it 2. click 2 3 6 (respectively) on the number pad on the right side of your keyboard 3. you release the ALT, and get ∞
SolomonZelman
  • SolomonZelman
try it yourself
anonymous
  • anonymous
anonymous
  • anonymous
thank you!
SolomonZelman
  • SolomonZelman
Yes, and if you use a the code 0 2 1 5 , you get ×
SolomonZelman
  • SolomonZelman
and code of 2 4 6 , you get ÷
SolomonZelman
  • SolomonZelman
there are many symbols like that. 755 , ≤ 754, ≥ 251, √
SolomonZelman
  • SolomonZelman
if you have any questions, I will be happy to answer.

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