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Question: Let f(x) = x – \(\frac{1}{2}\)log(x<sup>2</sup> + 1). Then f(x) is :...

Let f(x) = x – 12\frac{1}{2}log(x2 + 1). Then f(x) is :

A

Increasing for x > 0 only

B

Decreasing for x < 0 only

C

Increasing for all real x

D

Decreasing for all real x

Answer

Increasing for all real x

Explanation

Solution

f '(x) = 1 – 2x2(x2+1)\frac{2x}{2(x^{2} + 1)}= x2–x+1x2+1\frac{x^{2}–x + 1}{x^{2} + 1} > 0 ∀\forallxĪR

\ f(x) is increasing for all x Ī R.