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Assertion (A) : The maximum value of $\log_{1 / 3} (x^{2} - 4 x + 5)$ is $0$
Reason (R) : If $x > 0$ and $0 < a < 1$ then $\log_{a} x$ is a decreasing function

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A is false, R is true

Both A and R are true and R is the correct explanation of A

Both A and R are true and R is not the correct explanation of A

A is true, R is false

answer is B.

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Detailed Solution

$A : let f (x) = x^{2} - 4 x + 5 = {(x - 2)}^{2} + 1 \geq 1$

$\log_{1 / 3} x^{2} - 4 x + 5 = \log_{3^{- 1}} {(x - 2)}^{2} + 1 \geq - \log_{3} 1 \geq 0$

Min value = 0

$R : x > 0 0 < a < 1 \log_{a} x is decreasing$

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