Please help. Thanks!

Question

If 0 < a < 1, which of the following increases as a decreases?

a. a-1

b. a^2-1

c. 1/a

d. a^2

Answer 1

Answer (c) is the only choice with a in the denominator. So as a decreases, the denom gets smaller and 1/a increases because you're dividing by an ever-smaller number.

Answer 2

try plugging in some specific numbers, such as a=1/2 to a=1/4

A) a-1 goes from 1/2-1=-1/2 to 1/4-1 = -3/4 which decreases

B) a-1 goes from (1/2)^2-1= 1/4-1=-3/4 to (1/4)^2-1 = 1/16-1=-15/16 which is a decrease

C) a-1 goes from 1/1/2= 2 to 1/1/4= 4 which is an increase. C) is correct

D) is like B with a decrease