one to one functions g and h are defined as follows.
g={ (-9,7), (-1,-6), (1,4), (6,-1)}
h (x)= 2x-9

and I have to find the following of:
1.) g^-1 (-1) = ?
2.) h^-1 (x) =?
(h o h^-1) (1)= ?

(I don't understand the steps to finding these answers..)

Question

one to one functions g and h are defined as follows. 
g={ (-9,7), (-1,-6), (1,4), (6,-1)}
h (x)= 2x-9

and I have to find the following of:
1.) g^-1 (-1) = ?
2.) h^-1 (x) =?
(h o h^-1) (1)= ?

(I don't understand the steps to finding these answers..)

anonymous · Answer

The first question is to find "g inverse of -1"
which means you are looking for the number you would plug into g to get -1.
Looking at how the function g works, it seems that the answer is 6, because of the point (6, -1). This can be interpreted as g(6) = -1, so g inverse of -1 must be 6.

anonymous · Answer

so you are just switching the values since they are inverses?

anonymous · Answer

so for the h^-1 (x) it would be 4?

anonymous · Answer

sort of, basically, funtions and their inverses go "forwards" and "backwards"

as an example, one of the points in g is (-9, 7), so g(-9) = 7, while g inverse of (7) = -9

anonymous · Answer

ok i understand that but what am i supposed to do with the h (x)= 2x-9? I only use that when it asks a questions involving the h?

anonymous · Answer

for that "h inverse of x" problem its a little bit trickier. you are looking for a rule for the inverse; another function. the easiest way i know how to do this is to solve for x.  so:$$h(x) = 2x-9 \Longrightarrow h(x) +9 = 2x \Longrightarrow x = (h(x) +9)/2$$

anonymous · Answer

Then for formalities, switch the x and h(x), and change the h(x) to h inverse of x

anonymous · Answer

so i do the opposite of what it started out as?

anonymous · Answer

yeah, your doing the opposite of the the function is telling you to do

anonymous · Answer

btw the formal answer would be $$h^{-1}(x) = (x+9)/2$$

anonymous · Answer

ok so what happens on the (h o h^-1) (1)= ?  
 how do i figure out the h o h^-1 part... this part seems to be WAY more confusing

anonymous · Answer

would it just be the answer without switching anything since it is reversing twice? or no?

anonymous · Answer

Doing it by hand, that notation means you plug 1 into the inverse first and get an answer, then you plug that answer into the regular function, but since these functions are inverses of each other, it will spit out 1 as a final answer

anonymous · Answer

notice, h inverse of 1 is (1 + 9)/2 = 5
then h(5) is 2(5) - 9 = 1

anonymous · Answer

ok i think im understanding.. its just tricky. ill keep practicing with other problems now. THANK YOU