One-to-one functions

Question

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

g={(-8,-4), (-2,-7), (3,7), (7,3)}

h(x)=-x+13/5

Find the following.

(a) g^-1(7)

(b) h^-1(7)

(c) (h*h^-1(3)

Answer 1

g is (-8,-4), (-2,-7), (3,7), (7,3)

g^-1(x) = (-4,-8) (-7,-2), (7,3), (3,7)

just switch the x and y coordinates

h(x) = -x+13/5=y

switch x and y

-y +13/5 = x

solve for the new y

y = 13/5 -x = h^-1(x)

h(h^-1(3)) = 3

the composite of inverse functions brings you back to wear you started, in this case 3