Restrict the Domain of the Function F So That the Function

question 17

Multiple Choice

Restrict the domain of the function f so that the function is one-to-one and has an in- verse function. Then find the inverse function $f ^ { - 1 }$ . State the domains and ranges of f and $f ^ { - 1 }$ $f ( x ) = ( x - 4 ) ^ { 2 }$

• A) \(f ^ { - 1 } ( x ) = \sqrt { x } + 4\)
• The domain of \(f\) and the range of \(f ^ { - 1 }\) are all real numbers \(x\) such that \(x \geq 0\)
• The domain of \(f ^ { - 1 }\) and the range of \(f\) are all real numbers \(x\) such that \(x \geq 4\).
• B) \(f ^ { - 1 } ( x ) = \sqrt { x } - 4\)
• The domain of \(f\) and the range of \(f ^ { - 1 }\) are all real numbers \(x\) such that \(x \geq - 4\).
• The domain of \(f ^ { - 1 }\) and the range of \(f\) are all real numbers \(x\) such that \(x \geq 0\).
• C) \(f ^ { - 1 } ( x ) = \sqrt { x } + 4\)
• The domain of \(f\) and the range of \(f ^ { - 1 }\) are all real numbers \(x\) such that \(x \geq 4\).
• The domain of \(f ^ { - 1 }\) and the range of \(f\) are all real numbers \(x\) such that \(x \geq 0\).
• D) \(f ^ { - 1 } ( x ) = \sqrt { x } + 4\)
• The domain of \(f\) and the range of \(f ^ { - 1 }\) are all real numbers \(x\) such that \(x \geq 0\).
• The domain of \(f ^ { - 1 }\) and the range of \(f\) are all real numbers \(x\) such that \(x \geq - 4\).
• E) \(f ^ { - 1 } ( x ) = \sqrt { x } - 4\)
• The domain of \(f\) and the range of \(f ^ { - 1 }\) are all real numbers \(x\) such that \(x \geq 4\).
• The domain of \(f ^ { - 1 }\) and the range of \(f\) are all real numbers \(x\) such that \(x \geq 0\).

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Definitions:

Lumbar

Referring to the lower back region of the spine, encompassing the five vertebrae between the rib cage and the pelvis.

Sacrum

A large, triangular bone at the base of the spine and at the upper and back part of the pelvic cavity, formed by the fusion of five vertebrae.

Scoliosis

A medical condition characterized by an abnormal lateral curvature of the spine.

Lateral Curvature

Lateral curvature, often referring to scoliosis, is a condition characterized by a sideways curvature of the spine that deviates from the normal straight vertical alignment.