A PVT PLT ACCIDENTALLY ENTERED DFW CLASS B AIRSPACE WHILE ON FLT FOLLOWING WITH A DFW APCH CTLR. THE CTLR INTERVENED AND ASSIGNED THE PLT A HDG THAT WOULD TAKE THE ACFT OUT OF THE CLASS B AIRSPACE.

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FLYING VFR FROM TVK TO TPL AT 8500 FT USING FLT FOLLOWING. FLT FOLLOWING HAD GIVEN ME AN APCH FREQ AND I CONTACTED APCH. I WAS GIVEN A XPONDER CODE AND IDENTED. I GOT NO ANSWER. AFTER WAITING 5 MINS OR SO I CONTACTED APCH AND ASKED IF HE MADE RADIO CONTACT. HE SAID; 'JUST A MIN AND I'LL CHK.' HE REPLIED 'SARATOGA XYZ; RADAR CONTACT.' HE THEN HANDED ME OFF TO ANOTHER FREQ AND THAT CTLR TOLD ME TO TURN TO THE W; I HAD ENTERED CLASS B. I TURNED TO THE W AND AFTER 4 OR 5 MINS WAS HANDED TO ANOTHER FREQ AND CTLR. WHEN I CHKED IN HE SAID; 'YES; SARATOGA XYZ; WHAT'S YOUR REQUEST.' I SAID I HAD APPARENTLY ENTERED CLASS B AIRSPACE ACCIDENTALLY AND WAS VECTORED W AND WOULD LIKE TO TURN BACK ON MY COURSE HDG OF 179 DEGS WHEN POSSIBLE. HE ANSWERED 'COURSE HDG APPROVED; GO AHEAD AND MAKE YOUR TURN.' I THANKED HIM; TURNED ON COURSE AND CONTINUED ON TO TPL WITH FLT FOLLOWING. I AM A PLT OF ONLY 14 MONTHS AND REGRET THIS INCIDENT VERY MUCH AND NEXT TIME WILL MAKE SURE I HEAR THE WORDS 'CLRED TO ENTER'.