Question

The one-to-one functions g and h are defined as follows.

g={(-9, 2), (-1, -3), (2, 3), (9, 4)}
h(x) = 3x-4
Find the following.
g^-1 (2) =?
h^-1 (x) =?
(h • h^-1) (2) =?

Answer 1

Hello,

Explanation:

`g(-9)=2\Longrightarrow\ g^(-1)(2)=-9\\\\y=h(x)=3x-4\\x=3y-4\\\\y=(x+4)/(3) \\\\h^(-1)(x)=(x+4)/(3)\\\\h(h^(-1)(x))=(h^(-1)o\ h)(x)=1_\pi(x) \ (identical\ permutation\ of\ plane) \\\\h(h^(-1)(2))=2`