Question

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

g={(-7,-9),(-2,8),(2,-7),(3,2)}

h(x)=3x-10

Find the following.

g^-1 (2)=_____
h^-1 (x)= ______
(h•h^-1)(-1)=_____

Answer 1

The value of x, when y is 2 is 3.
Therefore, g^-1 (2) = 3

Let y = 3x - 10, then x = (y + 10)/3
Therefore, h^-1 (x) = (x + 10)/3

(h o h^-1)(x) = h(h^-1(x)) = h((x + 10)/3) = 3((x + 10)/3) - 10 = x.
Therefore, (h•h^-1)(-1) = -1