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