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Question: If f(x) and g(x) = \(f(x)\sqrt{1 - 2(f(x))^{2}}\) are monotonically increasing, then" x Î R...

If f(x) and g(x) = f(x)1−2(f(x))2f(x)\sqrt{1 - 2(f(x))^{2}} are monotonically

increasing, then" x Î R

A

| f (x)| £ 1

B

| f(x)| <23\frac{2}{3}

C

|f (x)| <12\frac{1}{2}

D

|f(x)| <12\frac{1}{\sqrt{2}}

Answer

|f (x)| <12\frac{1}{2}

Explanation

Solution

g¢ (x) = [1−4(f(x))2]f′(x)1−2(f(x))2\frac{\lbrack 1 - 4(f(x))^{2}\rbrack f'(x)}{\sqrt{1 - 2(f(x))^{2}}}

Now, as f(x) and g(x) are monotonically increasing,

f ¢(x) > 0 and g ¢ (x) > 0

̃ |f (x)| < 12\frac{1}{2}