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IPMAT Indore 2022 - QA (MCQ) Q27 Explanation
December 28, 2024
Explanation:
(a)
81^𝑥 + 81^𝑓(𝑥) = 3
Let 𝑓(𝑥) = 𝑦,
81^𝑥 + 81^𝑦 = 3
Or, 81^𝑥 = 3 − 81^𝑦
Now, 81^𝑥 will always be a positive number.
Means 81^𝑥 > 0
∴ 3 − 81^𝑦 > 0
⇒ 3 > 81^𝑦
⇒ 3 > 3^4𝑦
⇒ 1 > 4𝑦
(Property: If a is positive number & 𝑎^𝑥 > 𝑎^𝑦, then x > y)
⇒ 4𝑦 < 1
Or 𝑦 < 1/4.
∴ (−∞ 1/4 ) or, (−∞ 0.25)