The correct answer is: [A]: " f ⁻¹(x) = x + 2 " .
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Explanation:
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Given the function:
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" f(x) = x − 2 " ; find the "inverse function" ;
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Write as: " y = x − 2 " .
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Replace the "y" with "x" ; and the "x" with "y" ; and rewrite:
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" x = y − 2 " ;
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Now, solve for "y" ; and isolate "y" as a single variable, on the
"left-hand side" of the equation:
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↔ " y − 2 = x " ;
Now, add "2" to each side of the equation;
to isolate "y" on one side of the equation:
→ y − 2 + 2 = x + 2 ;
→ y = x + 2 ;
Now, replace the "y" ; with: " f ⁻¹(x) " ; and rewrite:
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→ " f ⁻¹(x) = x + 2 " ;
→ which is: Answer chioice: [A]: " f ⁻¹(x) = x + 2 " .
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