Uploaded August 2026 | Updated September 2026, 2 weeks ago

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Can you find the range of

f(x) = (2x - 3) / (2x² + 4x - 6) ?

This CAT 2025 Slot 3 question is a perfect example of why concepts matter more than relying on options.

The key idea:

f(x) = y
→ Convert it into a quadratic in x
→ For real x, D ≥ 0
→ Solve the resulting inequality
→ Use the number line and sign pattern
→ Get the exact range

For this question:

(8y - 1)(2y - 1) ≥ 0

The critical values are 1/8 and 1/2.

Using the +, −, + sign pattern:

y ≤ 1/8 or y ≥ 1/2

Hence,

Range = (-∞, 1/8] ∪ [1/2, ∞)

Correct Answer: Option 2

But remember — the question setter can change the options, change the condition, or make the question TITA.

CONCEPT IS KING.

Viewer Challenge:
Find the range of

g(x) = (4x + 4) / (x² + 8)

No options this time. Put your answer in the comments.

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