Let f(x) = x^2 − 81. Find f−1(x).

Question

anonymous · Answer

this one is different

kaitlyn_nicole · Answer

yeah, i thought so

anonymous · Answer

first off, it is not a one to one function, so it has no inverse, but never mind that, go ahead and solve $$x=y^2-81$$ for $y$

kaitlyn_nicole · Answer

how do i solve with two variables?

anonymous · Answer

the same way you would solve $$19=x^2-81$$

kaitlyn_nicole · Answer

o how'd you get 19?
or are you just putting in a random number

anonymous · Answer

add $81$, then take the square root of both sides, although your answer will have an $x$ in it

anonymous · Answer

i just picked a random number as an example

anonymous · Answer

the procedure would be the same for any number, and therefore any variable
add 81 take the square root

kaitlyn_nicole · Answer

ok, so x= y^2-81

anonymous · Answer

ok now add 81

kaitlyn_nicole · Answer

x-81=y^2

anonymous · Answer

hmm no

kaitlyn_nicole · Answer

i mean plus

anonymous · Answer

add, not subtract

anonymous · Answer

yeah that

kaitlyn_nicole · Answer

and then x+9=y?

anonymous · Answer

oh no!

kaitlyn_nicole · Answer

oo wat

anonymous · Answer

just write a square root sign over it

anonymous · Answer

$$x+81=y^2\
\pm\sqrt{x+81}=y$$

kaitlyn_nicole · Answer

ooooh snap

kaitlyn_nicole · Answer

you're really good at this lool

anonymous · Answer

now that $\pm$ out front means you do not have a function, so the question was in error

kaitlyn_nicole · Answer

oh okay, i was wondering what that meant.

anonymous · Answer

for $$f(x)=x^2-81$$ two different inputs will give the same output

anonymous · Answer

for example $$f(9)=81-81=0$$ and $$f(-9)=0$$ too 
so it does not have an inverse

kaitlyn_nicole · Answer

and they both fall on 0 so its not a function

anonymous · Answer

that is right
since $(9,0)$ and $(-9,0)$ are on the graph of $f$, the graph of $f^{-1}$ would have $(0,9)$ and also $(0,-9)$ one input with two different outputs, not a function

anonymous · Answer

where did this question come from, FLVS or sommat?

kaitlyn_nicole · Answer

flvs

kaitlyn_nicole · Answer

alg 2.

anonymous · Answer

BINGO!!

anonymous · Answer

got it on the first try
they really need to get their math act together down in Fla

kaitlyn_nicole · Answer

bingoooo

kaitlyn_nicole · Answer

yeah im really bad at math looool

anonymous · Answer

no it is not your fault at all

anonymous · Answer

you are asked bad questions, what can you do? 
don't they have any real schools near you?

danjs · Answer

i always think of the inverse switching the domain and range sets around

on the graph the two  look mirrored over the line y=x,  since all x and y swap to the other

reverses the function