Let \(f\) be a twice differentiable function defined on \(R\) such that \(f(0)=1, f^{\prime}(0)=2\) and \(f(x) \neq 0\) …

Let \(f\) be a twice differentiable function defined on \(R\) such that \(f(0)=1, f^{\prime}(0)=2\) and \(f(x) \neq 0\) for all \(x \in R\). If \(\left|\begin{array}{ll}f(x) & f^{\prime}(x) \\ f^{\prime}(x) & f^{\prime \prime}(x)\end{array}\right|=0\), for all \(x \in R\), then the value of \(f(1)\) lies in the interval.

[JEE Main 2021, 24 Feb (Shift 2)]