MonotonicityHard
Question
Let continuous functions f1(x) & f2(x) are two values of f(x) for which equation |f(x) - x| = xln(x - 1) holds. If f1 (3) > 2, then -
Options
A.f1(x) is an increasing function
B.f2(x) is a decreasing function
C.f1(x) is a decreasing function
D.f2(x) is an increasing function
Solution
f(x) 
⇒ f(x) =
f′(x) = 1 +
+ ln(x - 1) > 0 ∀ x ≥ 2
f′(x) = 1 -
- ln(x - 1) < 0 ∀ x ≥ 2
⇒ f1(x) = x + xln(x - 1) & ↑
f2(x) = x - xln(x - 1)& ↓
⇒ f(x) =
f′(x) = 1 +
+ ln(x - 1) > 0 ∀ x ≥ 2f′(x) = 1 -
- ln(x - 1) < 0 ∀ x ≥ 2⇒ f1(x) = x + xln(x - 1) & ↑
f2(x) = x - xln(x - 1)& ↓
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