Application Of Derivatives

If \(g(x)=\frac{1}{6} f\left(3 x^2-1\right)+\frac{1}{2} f\left(1-x^2\right), \forall x \in R\), where \(f^{\prime \prime}(x) > 0, \forall x \in R\). Then, \(g(x)\) is increasing in the interval