Question

For the function 32/x+3, find (g^-1∘ g)(5).


11
5
1
2

Answer 1

what do you think ?

Answer 2

and by g^-1 you mean inverse of g ?

Answer 3

I guess , lol . Thats how the question looks.

Answer 4

ok.. so what do you think is the answer ?
in general what is the result of the composition of inverse of a function with the function ?

Answer 5

I have no idea , I worked it out and got 4 . lol But i guess I didn't work it out right .

Answer 6

g^-1∘ g is like
g^-1(g(x)
right ?

Answer 7

right .

Answer 8

now when we plug the real function into the inverse of the function we really get back x

Answer 9

it is because that if we have for example f(x)
and we plug into it 5 we get f(5)

and for the inverse f^-1(x)
when we plug f(5)
we get 5

Answer 10

do you understand what i mean ?

Answer 11

Kinda. I'm just kinda lost.

Answer 12

lets do it with an example

x^2

plug 5 :
f(5) = 25

now lets look for f^-1(x)
it is sqrt(x)

now plug in there 25
we get
sqrt(25) = 5

Answer 13

this is an example of a general property.. f^-1(f(x)) = x

Answer 14

oh , i understand a little bit better.

Answer 15

the real function takes a value from the domain and returns the corresponding value from the range

the inverse take a value from the range and returns the corresponding value from the domain

Answer 16

so if you took x and plug it into f(x) you got f(x)
(domain) (range)


now you plug f(x) into f^-1(x) and you got x back
(range) (domain)

Answer 17

im feeling like im saying the same thing but i hope it helps

Answer 18

your not , im understanding. i just have to take a second to think about it. so the answer is 5 ?

Answer 19

yes

Answer 20

Thank you sooo much . ! (:

Answer 21

youre welcome :)