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The one-to-one functions and are defined as follows.?

+3 votes

 

g={(-8,-2),(-1,7),(3,-1),(9,3)}
h(x)=3x+2

find
g^-1(-1)=?
h^-1(x)=?
(h o h^-1) (8)=

 

asked Jan 2, 2013 in PRE-ALGEBRA by linda Scholar

2 Answers

+3 votes
ii) Given function h(x) = 3x+2.
let h(x) = y then x = h^-1(y)
y = 3x+2
 
Siubtract 2 from each side
y - 2 = 3x + 2 - 2
 
Additive inverse property: 2 - 2 = 0
y - 2 = 3x
 
Divide each side by 3
(y - 2)/3 = 3x/3
 
Cancel common terms
x = (y - 2)/3
 
Then h^-1(y) = (y - 2)/3
          h^-1(x) = (x - 2)/3
 
iii) (h o h^-1) (8) = h(h^-1(8))
h^-1(x) = (x - 2)/3 then h^-1(8) = (8 - 2)/3
                                                = 6/3
                                                = 2
 
Substitute h^-1(8) = 2 in (h o h^-1) (8)  then
h(x) = 3x+2
 
Substitute x = 2
h(2) = 3(2)+2
        = 6+2
        = 8
answered Jan 2, 2013 by peterson Rookie
0 votes

i) g = {(-8,-2),(-1,7),(3,-1),(9,3)} which means that g(-8) = -2, g(-1) = 7, g(3) = -1 and g(9) = 3.

Therefore g-1 = {(-2,-8),(7,-1),(-1,3),(3,9)} which means that g-1(-2) = -8, g-1(7) = -1, g-1(-1) = 3 and g-1(3) = 9.

We have to find g-1(-1) which is 3.

Therefore g-1(-1) = 3.

answered Jun 26, 2014 by joly Scholar

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