Question

If r(x) = 2 – x2 and w(x) = x – 2, what is the range of (w*r)(x)

Answer 1

is it ` (wº r)(x) `, or is it ` (w • r)(x) ` ?

Answer 2

the first one

Answer 3

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.

Answer 4

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

Answer 5

can you simplify the w(r(x)) /

Answer 6

?

Answer 7

do you mean solve (w-x^2)-2?

Answer 8

2 instead of w

Answer 9

my bad

Answer 10

if so it would be -x^2

Answer 11

yes

Answer 12

so
(wº r)(x) = -x²

and you need to find the range of this

Answer 13

ok and how would i do that haha

Answer 14

x² \(\small \ge\) 0

(for any real number value of x)

Answer 15

so the range of x² is (0,+∞)

Answer 16

now, multiply both sides of:
x² \(\small \ge\) 0

by -1, and you get

Answer 17

-x^2 and 0

Answer 18

and what is the sign, \(\small \ge\) or \(\small \le\)

Answer 19

<

Answer 20

-x² \(\small \le\) 0

like that?

Answer 21

yes

Answer 22

that is correct

Answer 23

yay ty

Answer 24

so -x² is at most 0, and can go into any very big negative values

Answer 25

mhm

Answer 26

so the range of -x² is?

Answer 27

well, it is at most 0, so we know that:
,0]

and it can go into nagetive infinty so we know that:
(-∞, 0]

Answer 28

thats it

Answer 29

yes

Answer 30

i just didnt know how to make a infinity sign haha

Answer 31

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 ∞

Answer 32

try it yourself

Answer 33

∞

Answer 34

thank you!

Answer 35

Yes, and if you use a the code
0 2 1 5 , you get
×

Answer 36

and code of 2 4 6 , you get ÷

Answer 37

there are many symbols like that.
755 , ≤
754, ≥

251, √

Answer 38

if you have any questions, I will be happy to answer.