Question

@speedygonzalles can you help me please

Let f(x) = x^2 - 81 find f^1(x)

Answer 1

to find the inverse of a function
replace x with y and y with x
so x = y^2 - 81 solve for y

Answer 2

would i add 81 to y^2?

Answer 3

?

Answer 4

mmm if by add you mean
x = y^2 - 81
+81 +81
then yes :P

Answer 5

so it would be 81x =y^2 do i divide 81 by 2 now?

Answer 6

not quite :)
what I did was addition
so you would get x + 81 = y^2 so you would then square root both sides

Answer 7

so it would be x + 9 = y^2?

Answer 8

i dont know what to do with y^2

Answer 9

square rooting both sides would make y^2 turn into y
and (x+81) with a square root over it

Answer 10

would that make it ±sqrt x plus 81?

Answer 11

correct :)

Answer 12

thank you so much can you help me with a couple more?

Answer 13

of course :)

Answer 14

Thank you!

my next problem is Let f(x) = x + 8 and g(x) = x2 - 6x - 7. Find f(g(2)).

Answer 15

i think i would do f(g(2)) = x + 8 is that right?

Answer 16

not quite :)

first you should find g(2) = ?

Answer 17

ok how would i do that is it f(g(2)) = x + 8 g(x) = 2x - 6x -7?

Answer 18

im not sure how to set the problem up im sorry

Answer 19

is this the same problem? :/

Answer 20

yes its my 2nd question its not the same as the sqrt81 problem

Answer 21

I was getting a little confused because "f(x) = x + 8 and g(x) = x2 - 6x - 7. Find f(g(2))." was not the same as "f(g(2)) = x + 8 g(x) = 2x - 6x -7?"

Answer 22

oh im sorry i didnt mean to confuse you

Answer 23

mmm alright
the over all method to doing a f(g(n)) problem
would be to first plug in n (number) into g(x)
to get another number
which you would then plug in to f(x)
and simplify to get your answer

Answer 24

but i dont know what to plug into my problem

Answer 25

well they want you to find f(g(2)) right?
so then plug in 2 into g(x)

Answer 26

would it be f(x + 8) = g(x2 - 6 -7)

Answer 27

whoa there...
is it "f(x) = x + 8 and g(x) = x2 - 6x - 7. Find f(g(2))." that you're looking for?

then you just need to find g(2) first

Answer 28

yes that is my problem so since i only have to find g(2) would i do g(x2 -6 - 7)?

Answer 29

not quite :)
g(2) means to plug in 2 for x into x^2 - 6x - 7

Answer 30

ok:) so would it be x^2 -6x -7?
and if so would my next step be +7 to both sides? im sorry i hope im not being to much of a pain algebra for some reason is really hard for me to grasp

Answer 31

it's alright :)
mmm do you know what to plug in 2 for x means? :/

Answer 32

does it mean it is now 2x?

Answer 33

or would it mean x = 2

Answer 34

yes x = 2 is what I mean :)

Answer 35

so would my equation be 2x^2 -6x -7?

Answer 36

mmm more like (2)^2 - 6(2) - 7 and simplify using PEMDAS

Answer 37

ok:) can you tell me if this is right?
(2)^2 - 6(2) - 7
4 - 12 -7
+4 +4
-12 -3 / 3 = -4?

Answer 38

not quite :) you're over thinking this :P
just do 4 - 12 - 7 like a calculator would


(sorry but my internet died, so I might be slower at responding)

Answer 39

-15?

Answer 40

Correct! :)
then plug in -15 into x+8
so -15 + 8 = ?

Answer 41

-7?

Answer 42

Yes! :D tah-dah! ^_^

Answer 43

Thank you so much!!! can i open a new question and tag you in it?

Answer 44

sure :)