Functions
Functions
Allen Star Batch
Grade 12

Question:

The reflection about the line $x + y = 0$ of the inverse function $f^{-1}(x)$ of a function $f(x)$ is:
$-f(x)$
$-f(-x)$
$-f^{-1}(x)$
$-f^{-1}(-x)$

Step-by-Step Solution

Key Concept: Reflection about the line x + y = 0 (or y = -x) swaps coordinates and negates them: point (a, b) maps to (-b, -a). For the inverse function f⁻¹(x), if (x, y) lies on its graph, then (-y, -x) lies on the reflected graph, yielding the transformation y = -f(-x).
Check by drawing a rough graph of the function to verify its properties visually.
Correct Answer: 2

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