For Any Function F: a → B , Define a New

question 18

Essay

For any function f: A → B , define a new function g: P(A) → P(B) as follows: for every S ⊆ A, g(S) = { f(x) |
x ∈ S Prove that f is onto if and only if g is onto.

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Definitions:

Vascular Response

The series of changes in the size and calibre of blood vessels in reaction to stimuli, affecting blood flow and pressure.

Antidiuretic Hormone

A hormone produced by the brain that regulates the balance of water in the body by reducing the amount of water excreted in urine.

Alarm Stage

The initial phase of the body's response to stress, activating the fight-or-flight response.

Fluid Retention

The accumulation of excess water in the tissues of the body, often leading to swelling, known medically as edema.