Speed Racer is an 18-year-old whose life and love has always been automobile racing. His parents Pops and Mom run the independent Racer Motors, in which his brother Spritle, mechanic Sparky, and girlfriend Trixie are also involved. As a child Speed idolized his record-setting older brother, Rex Racer, who was killed while racing in the Casa Cristo 5000, a deadly cross-country racing rally. Now embarking on his own career, Speed Racer is quickly sweeping the racing world with his skill behind the wheel of his brother's cars, the Mach 5 and his own Formula One car the Mach 6, but remains primarily interested in the art of the race and the well-being of his family.
E.P. Arnold Royalton, owner of conglomerate Royalton Industries, offers Speed an astoundingly luxurious lifestyle in exchange for signing to race with him. Speed is tempted but declines due to his father's distrust of power-hungry corporations. Angered, Royalton reveals that for many years the key races have been fixed by corporate interests, including Royalton himself, to gain profits. Royalton takes out his anger on Speed by having his drivers force Speed into a crash that destroys the Mach 6 and suing Racer Motors for intellectual property infringement. Speed gets an opportunity to retaliate through Inspector Detector, head of a corporate crimes division. Racer Taejo Togokahn says that he has evidence that could indict Royalton but will only offer it up if Speed and the mysterious masked Racer X agree to race on his team in the Casa Cristo 5000. Taejo says that a win could substantially raise the stock price of his family's racing business, blocking a Royalton-arranged buyout. Speed agrees but keeps his decision secret from his family, and Inspector Detector's team makes several defensive modifications to the Mach 5 to assist Speed in the rally.
After they drive together and work naturally as a team, Speed begins to suspect that Racer X is actually his brother Rex in disguise. His family discovers that he has entered the race and agree to support him. With the help of his family and Trixie, Speed defeats many brutal racers who have been bribed by fixer Cruncher Block to stop him, and overcomes seemingly insurmountable obstacles to win the race. However, Taejo's arrangement is revealed to be a sham, as he was only interested in increasing the value of his family's company so that they could profit from Royalton's buyout. An angry Speed hits the track that he used to drive with his brother, and confronts Racer X with his suspicion that he is Rex. Racer X removes his mask, revealing an unfamiliar face, and tells Speed that Rex is indeed dead. Speed returns home, where Taejo's sister Horuko Togokahn gives him Taejo's automatic invitation to the Grand Prix, which Taejo had rejected. The Racer family bands together and builds the new Mach 6 in 32 hours.
Speed enters the Grand Prix against great odds: Royalton has placed a bounty on his head that the other drivers are eager to collect, and he is pitted against future Hall of Fame driver Jack "Cannonball" Taylor. Speed overcomes a slow start to catch up with Taylor, who uses a cheating device called a spearhook to latch the Mach 6 to his own car. Speed uses his jump jacks to expose the device to video cameras, causing Taylor to crash. Speed wins the race, having successfully exposed Royalton's crimes. While Racer X watches it is revealed in a flashback montage that he really is Rex, who has faked his death and undergone plastic surgery to change his appearance as part of his plan to save his family and the sport of racing. He chooses not to reveal his identity to his family, declaring that he must live with his decision. The Racer family celebrates Speed's victory as Speed and Trixie kiss, and Royalton is sent to jail.

Question: How does Speed get an invitation to the Grand Prix?
Answer: He is given the invitation Taejo rejected by Taejo's sister Horuko
Alternative answer: He accepts Tajeo's rejected invitation to the Grand Prix.