SOLUTION: This problem is giving me a hard time, please help! The one-to-one functions g and h are defined as follows. =g{(−7, 1), (1, -7), (5, 6), (7, 9)} =h(x)=3x-14 F

Algebra ->  Trigonometry-basics -> SOLUTION: This problem is giving me a hard time, please help! The one-to-one functions g and h are defined as follows. =g{(−7, 1), (1, -7), (5, 6), (7, 9)} =h(x)=3x-14 F      Log On


   

Question 1062663: This problem is giving me a hard time, please help!
The one-to-one functions g and h are defined as follows.
=g{(−7, 1), (1, -7), (5, 6), (7, 9)}

=h(x)=3x-14
Find:
g^-1(1)=
h^-1(x)=
(h^-1 º h)(7)=
Answer by Fombitz(32388) About Me  (Show Source):
You can put this solution on YOUR website!
The inverse of g uses the range of g as the domain so, using g, find the x value corresponding to the y value of 1, y=-7, so,
g%5E%28-1%29%281%29=-7
.
.
.
To find the inverse of h, use x,y nomenclature,
y=3x-14
Interchange x and y and solve for y.
This new y is the inverse.
x=3y-14
3y=x%2B14
y=%28x%2B14%29%2F3
h%5E%28-1%29%28x%29=%28x%2B14%29%2F3
.
.
.
The composition of a function and its inverse yields the original input.
h%5E%28-1%29%28h%28x%29%29=x
So then,
h%5E%28-1%29%28h%287%29%29=7
or
3%28%28x%2B14%29%2F3%29-14=%28x%2B14%29-14=x