SOLUTION: The one-to-one functions g and h are defined as follows. g = {(-7,4), (4,-7), (8,5), (9,-4)} h(x) = 3x-13 Find the following. g^-1(-7) = h^-1(x) = (h*h^1)(8) =

Algebra ->  Equations -> SOLUTION: The one-to-one functions g and h are defined as follows. g = {(-7,4), (4,-7), (8,5), (9,-4)} h(x) = 3x-13 Find the following. g^-1(-7) = h^-1(x) = (h*h^1)(8) =      Log On


   

Question 1138783: The one-to-one functions g and h are defined as follows.
g = {(-7,4), (4,-7), (8,5), (9,-4)}
h(x) = 3x-13
Find the following.
g^-1(-7) =
h^-1(x) =
(h*h^1)(8) =
Answer by adamsmith9037(4) About Me  (Show Source):
You can put this solution on YOUR website!
g^-1(-7) = 4 (note that inverse functions swap the x and y coordinates and the
coordinate (4,-7) is swapped to (-7,4)
h^(-1)x=....
let y = 3x-13
swapping the x and y,
x = 3y-13
making y the subject of the equation,
y = (x+13/3)
and hence h^(-1)x=(x+13/3)
h(x) = 3x-13
h(h(x)) = 3(3x-13) - 13
h(h(x)) = 9x - 39 - 13
h(h(x)) = 9x - 52
when x = 8,
9(8) - 52 = 72 - 52 = 20