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​Q. IF f ( x ) IS A DIFFERENTIABLE FUNCTION AND f ’ ( x ) = log 1/3 ( log 3 ( sin x + a) ) , THEN FIND THE INTERVAL OF ‘’a’’ SO THAT f ( x ) IS DECREASING FOR ALL REAL VALUES OF x .

​Q. IF f ( x ) IS A DIFFERENTIABLE FUNCTION AND f ( x ) = log1/3 ( log3 ( sin x + a) ) , THEN FIND THE INTERVAL OF ‘’a’’ SO THAT f ( x ) IS DECREASING FOR ALL REAL VALUES OF x .

Grade:Select Grade

2 Answers

Jitender Singh IIT Delhi
askIITians Faculty 158 Points
6 years ago
Ans:
Hello Student,
Please find answer to your question below

If the f(x) is decreasing, then
f'(x) < 0
log_{1/3}(log_{3}(sinx+a)) < 0
log_{1/3}(log_{3}(sinx+a)) < log_{1/3}1
log_{3}(sinx+a) > 1
log_{3}(sinx+a) > log_{3}3
sinx+a > 3
a > 3 - sinx............(1)
Also for the domain of logarithm function,
sinx + a > 0
a > -sinx…......(2)
Combining (1) and (2) we have
a > 3-sinx
Since x belong to R,
a > 2


Bharat Makkar
34 Points
6 years ago
but i think a > 4 as a =3 doesnt satisfy the equation.

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