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