Question

URGENT!!!: What is the range of f^-1[g(x)]???

Answer 1

Maybe @triciaal or @jim_thompson5910 could help :)

Answer 2

There seems to be missing information. Can you post a screenshot?

Answer 3

ok one sec

Answer 4

here!!

Answer 5

so this is all part of #6 and

\[\Large f(x) = \frac{2}{x+3}\]
\[\Large g(x) = 2^{x-1}\]

right?

Answer 6

yes

Answer 7

im stuck on part b). i have the domain i just cant figure out the range

Answer 8

I agree that

\[\Large f^{-1}(x) = \frac{2-3x}{x}\]
\[\Large f^{-1}(g(x)) = \frac{2-3(2^{x-1})}{2^{x-1}}\]

Answer 9

you have the correct domain as well

Answer 10

as for the range, let me think

Answer 11

ok

Answer 12

\[\Large f^{-1}(x) = \frac{2-3x}{x}\]

\[\Large f^{-1}(x) = \frac{2}{x} - \frac{3x}{x}\]

\[\Large f^{-1}(x) = \frac{2}{x} - 3\]

\[\Large f^{-1}(g(x)) = \frac{2}{2^{x-1}} - 3\]

Answer 13

as x gets larger and larger, the term \(\LARGE \frac{2}{2^{x-1}}\) gets smaller and smaller effectively getting to small that it becomes 0

Answer 14

so as x gets larger and larger

\[\Large f^{-1}(g(x)) = \frac{2}{2^{x-1}} - 3\]

gets closer and closer to -3. It will never actually get to -3 itself though

Answer 15

does that make sense?

Answer 16

wait so whats the range?

Answer 17

if you plug in x = 0, what do you get?

Answer 18

idont know :(((((

Answer 19

@triciaal

Answer 20

\[\Large f^{-1}(g(x)) = \frac{2}{2^{x-1}} - 3\]

\[\Large f^{-1}(g(0)) = \frac{2}{2^{0-1}} - 3\]

\[\Large f^{-1}(g(0)) = ???\]

Answer 21

consider when x is negative
when x = 0 and when x is positive

Answer 22

you said you had the actual domain
the range is the set of y values

Answer 23

can i pls just have the answer pls. this homework q is the last one and im rly tired plz

Answer 24

maybe -infinity to -3 not sure

Answer 25

ok thanks

Answer 26

if you graph the entire thing, you'll get this

Answer 27

it goes up forever but doesn't do the same in the other direction. Instead it gets closer and closer to -3 (but never actually gets to -3)

so the range is y > -3 which in interval notation is (-3, infinity)

Answer 28

omg thank you guys so much

Answer 29

no problem

Answer 30

i can finally sleep!!!!!

Answer 31

I see my error when x = -infinity y is positive so the solution is like Jim has it

Answer 32

guys!!!

Answer 33

is anyone here still able to help me with one more q?

Answer 34

go ahead