Question

I GIVE MEDALS AND FAN!

Answer 1

The inverse of the function y = 9 - x 2, for all values x ≥ 3, is _____, where x can take values _____.

Show your work

Answer 2

First you check if horizontal like test work! for \(x \ge 3\)

Answer 3

so you need to graph that function and see first

Answer 4

Okay so how do I graph it?

Answer 5

line*

Answer 6

well have ever graphed quadratic function
the shifting, up down reflection thingy?

Answer 7

I think I remember some things but not really.

Answer 8

well you will need to check that out later!
for now check how this graph looks like
http://fooplot.com/#W3sidHlwZSI6MCwiZXEiOiI5LXheMiIsImNvbG9yIjoiIzAwMDAwMCJ9LHsidHlwZSI6MTAwMCwid2luZG93IjpbIi0zLjY3OTk5OTk5OTk5OTk5OTciLCI5LjMyIiwiLTQuMzgiLCIzLjYyMDAwMDAwMDAwMDAwMSJdfV0-

Answer 9

we only interested in the part x>=3

Answer 10

Okay

Answer 11

the graph looked something like that
so does this pass the horizontal line test

Answer 12

No?

Answer 13

why not!

Answer 14

does the horizontal like cuts in more than one point?

Answer 15

Oh yeah.

Answer 16

So what's the answer?

Answer 17

passes or not?

Answer 18

Yes.

Answer 19

Ok, no we can safely go for inverse of this function that satisfies this characteristics

Answer 20

So?

Answer 21

y=9-x^2
switch the x and y
x=9-y^2
then solve for y
y^2=9-x
square root both sides
\(\huge y=\sqrt{9-x}\) since we taking only the positive y
we don't need the negative root
So \(\large f^-1(x)=\sqrt{9-x}\)

Answer 22

so the domain is 9-x>=0
x<=9
so the values that x can take are x<=9

Answer 23

f^-1 above is f inverse alright!

Answer 24

So what would I write in the first blank?

Answer 25

well i give you the answer already! this means you don't get yet?

Answer 26

Would it be the domain? Cause I know the second blank would be x<=9.

Answer 27

The domain?
first blank is asking for f inverse not domain!

Answer 28

Can't you see that i gave you the f inverse above?

Answer 29

So??

Answer 30

Yeahh. I got it now. Thanks.

Answer 31

you are welcome!