Problem: If f(x)=3x+2 for all real x, then the statement: "∣f(x)+4∣<a whenever ∣x+2∣<b and a>0 and b>0" is true when
Answer Choices:
A. b⩽a/3
B. b>a/3
C. a⩽b/3
D. a>b/3
E. The statement is never true
Solution:
Consider ∣f(x)+4∣=∣3x+2+4∣=3∣x+2∣. Now whenever ∣x+2∣<3a, then ∣f(x)+4∣<a.
Consequently whenever ∣x+2∣<b and b≤3a, we have ∣f(x)+4∣<a.