Find the Inverse Of $f$ Then Sketch the Graphs Of Then

question 30

Multiple Choice

Find the inverse of $f$ . Then sketch the graphs of $f$ and $f ^ { - 1 }$ on the same set of axes.
$f ( x ) = \sqrt { 16 - x ^ { 2 } } , x \geq 0$

• A) \(f^{-1}(x)=\sqrt{4+x^{2}}, x \geq 0\)
• B) \(f ^ { - 1 } ( x ) = - \sqrt { 16 - x ^ { 2 } } , x \geq 0\)
• C) \(f ^ { - 1 } ( x ) = \sqrt { 16 - x ^ { 2 } } , x \geq 0\)
• D) \(f ^ { - 1 } ( x ) = - \sqrt { 4 + x ^ { 2 } } , x \geq 0\)

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Definitions:

Bromobenzene

An aromatic bromine compound used frequently in organic synthesis, as a bromination precursor for making various organic products.

Benzenesulfonic Acid

An organosulfur compound characterized by a benzene ring bonded to a sulfonic acid group, used in various chemical syntheses.

Bromination

A chemical reaction involving the addition of bromine to another substance, often leading to the substitution or addition of bromine atoms in organic compounds.

Toluene

A colorless, water-insoluble liquid hydrocarbon (C7H8) derived from coal tar or petroleum, used as a solvent and in the manufacture of various chemicals.