In this paper, we obtain the Fekete-Szegö problem for the k-th (k ≥ 1) root transform of the analytic and normalized functions f satisfying the condition 1 + α − π 2 sin α < Re z f (z) f (z) < 1 + α 2 sin α (|z| < 1), where α ∈ [π/2, π). Afterwards, by the above two-sided inequality we introduce a certain subclass of analytic and bi-univalent functions in the disk |z| < 1 and obtain upper bounds for the first few coefficients and Fekete-Szegö problem for functions f belonging to this class