The Function F Is One-To-One $$f ( x ) = x ^ { 2 } + 1 , x \geq 0$$

question 144

Multiple Choice

The function f is one-to-one. Find its inverse.
- $$f ( x ) = x ^ { 2 } + 1 , x \geq 0$$

• A) \(\mathrm { f } ^ { - 1 } ( \mathrm { x } ) = \sqrt { \mathrm { x } } - 1 , \mathrm { x } \geq 0\)
• B) \(f ^ { - 1 } ( x ) = \sqrt { x - 1 } , x \geq 1\)
• C) \(\mathrm { f } ^ { - 1 } ( \mathrm { x } ) = \sqrt { \mathrm { x } + 1 } , \mathrm { x } \geq - 1\)
• D) \(\mathrm { f } ^ { - 1 } ( \mathrm { x } ) = \sqrt { \mathrm { x } } - 1 , \mathrm { x } < 0\)

---

Definitions:

Gestalt Concept

A principle in psychology that describes the human ability to perceive patterns or wholes in complex visual inputs instead of merely additive sensory inputs.

Closure

A psychological phenomenon where the mind seeks to perceive a complete image or idea even when certain components are missing or incomplete.

Kinesthetic

Relates to the perception of body position and movement, often referred to as muscle sense.

Vestibular Senses

The sensory system that contributes to balance and spatial orientation by detecting changes in motion and gravitational pull.