A function g(x) is defined as \[g(x)=\frac{1}{4}f(2{{x}^{2}}-1)+\frac{1}{2}f(1-{{x}^{2}})\] and \[f(x)\] is an increasing function. Then g(x) is increasing in the interval

\[\left( -\sqrt{\frac{2}{3}},\sqrt{\frac{2}{3}} \right)\]

\[\left( -\sqrt{\frac{2}{3},}0 \right)\cup \left( \sqrt{\frac{2}{3}},\infty \right)\]

A function g(x) is defined as \[g(x)=\frac{1}{4}f(2{{x}^{2}}-1)+\frac{

1.	A function g(x) is defined as \[g(x)=\frac{1}{4}f(2{{x}^{2}}-1)+\frac{1}{2}f(1-{{x}^{2}})\] and \[f(x)\] is an increasing function. Then g(x) is increasing in the interval
A.	\[(-1,1)\]
B.	\[\left( -\sqrt{\frac{2}{3},}0 \right)\cup \left( \sqrt{\frac{2}{3}},\infty \right)\]
C.	\[\left( -\sqrt{\frac{2}{3}},\sqrt{\frac{2}{3}} \right)\]
D.	None of these
Answer» C. \[\left( -\sqrt{\frac{2}{3}},\sqrt{\frac{2}{3}} \right)\]

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A function g(x) is defined as \[g(x)=\frac{1}{4}f(2{{x}^{2}}-1)+\frac{1}{2}f(1-{{x}^{2}})\] and \[f(x)\] is an increasing function. Then g(x) is increasing in the interval

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