To find the inverse of the function g(x):
g(x) = (x - 8)/7
1. Replace g(x) with y:
y = (x - 8)/7
2. Solve for x in terms of y:
7y = x - 8
x = 7y + 8
3. Replace x with g^-1(x):
g^-1(x) = 7x + 8
To find (g^-1 • g)(1):
1. Substitute x = 1 into g(x):
g(1) = (1 - 8)/7 = -7/7 = -1
2. Substitute -1 into g^-1(x):
g^-1(-1) = 7(-1) + 8 = 1
Therefore, (g^-1 • g)(1) = 1.
To find h^-1(5):
h = {(-9,-8),(-2,5),(4,0),(5,2)}
1. Look for the pair (5,2) in h.
2. Swap the x and y values to get the inverse pair:
h^-1(5) = (2,5)
Therefore, h^-1(5) = (2,5).