"given purpose" is correct and usable in written English.
It is often used to refer to a specific intention or goal. For example, "They conducted the experiment for the given purpose of testing the efficacy of the new medication."
The book dealer's life has always been given purpose by the possibility of such serendipitous, almost magical, discoveries.
In silos, in submarines, in nocturnal repose, the beast, the nuclear beasts, the golems, waiting to be triggered into life, to be given purpose, to be given soul.
But the gravity of the threat alone cannot be dispositive of questions concerning what means law enforcement officers may employ to pursue a given purpose.
America's food and drug law does not say that a drug has to be better than its competitors for a given purpose to be licensed.
But one cabal with a sinister agenda of Germanic supremacy has given purpose to a serial killer whose terrible handiwork leads Inspector Oskar Rheinhardt to consult with his friend, the psychologist Max Liebermann, on a clinical profile of the murderer.
FOR most of four decades, the Z-car has given purpose and direction to the rest of Nissan's lineup, serving as a metallic lodestar for engineers toiling away on ambitious sedans like the Altima and Maxima.
They also urged Mr. Bush to eliminate a section of the rules that says health care providers cannot use any personal medical information beyond the "minimum necessary" to accomplish a given purpose.
She has given purpose to many people, and when the governor and his daughter arrive to pay tribute, the officers are thrilled when they are asked to work security.
Aomame's strangely passive life, in which she administers death to her victims with a single sterile needle applied to a point at the base of the brain, is only given purpose, we come to learn, by the memory of a single act of affection.
