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

Question

g={(-1,-5), (1,3), (3,8), (6,-1)}

h(x)=2x-3

Find the following.

g^-1(-1)=

h^-1(x) =

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

Answer 1

G_inverse (-1) = 6 since G maps 6 to -1

y = H(x) = 2x-3

x = 2y - 3

(x+3) = 2y

(x+3)/2 = y = H_inverse

H_inverse(3) = (3+3)/2 = 6/2 = 3

H(3) = 2*3-3 = 6-3=3

So

H comp H_inverse (3) = H (3) = 3