The lower-bound conjecture for the induced-forest ratio

Let $G$ be a graph with minimum degree $\delta(G)\geq 2$. Define $t(G)$ as the minimum size of a vertex set whose deletion leaves an induced forest, let $\operatorname{LIF}(G)$ denote the maximum order of an induced forest in $G$, and set

$$f(G)=\frac{\operatorname{LIF}(G)}{t(G)}.$$

Lower-bound conjecture. If $G$ has minimum degree at least $2$, then

$$f(G)\geq 2.$$

This conjecture is motivated by exhaustive computations for graphs of order at most $10$ and minimum degree at least $2$, which support the proposed universal lower bound.