a. 2^(x-2) = g^(-1)(x)
b. A, B, D
Step-by-step explanation:
the phrasing attached in the image is flagged as inappropriate, so i will be replacing it with g(x) and its inverse with g^(-1)(x)
1. replace g(x) with y and solve for x
y = log₂(x) + 2
subtract 2 from both sides to isolate the x and its log
y - 2 = log₂(x)
this text is replaced by the second image -- it was marked as inappropriate
thus, 2^(y-2) = x
replace x with g^(-1)(x) and y with x
2^(x-2) = g^(-1)(x)
2. plug this in to points A, B, C, D, E, and F
A: (2,1)
plug 2 in for x
2^(2-2) = 2⁰ = 1 so this works
B: (4, 4)
2^(4-2) = 2²= 4 so this works
C: (9, 3)
2^(9-2) = 2⁷ = 128 ≠ 3 so this doesn't work
(5, 8)
2^(5-2) = 2³ = 8 so this works
E: (3, 5)
2^(3-2) = 2¹ = 2 ≠ 5 so this doesn't work
F: (8, 5)
2^(8-2) = 2⁶ = 64 ≠ 5 so this doesn't work