if $f$ is measurable real valued function on $E \subseteq \mathbb{R}^n$ then $f^{-1} (B)$ is borel set for every borel set in $\mathbb{R}$?

Question

I am trying to find a counterexample to show that not necessary if $f$ is measurable real valued function on $E \subseteq \mathbb{R}^n$ then $f^{-1} (B)$ is borel set for every borel set in $\mathbb{R}$. I know that if $f$ is countinous then $f^{-1} (B)$ is borel set for every borel set in $\mathbb{R}$. and we know if $f$ is measurable not necessary to be measurable.