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 .

Question

​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 .

Jitender Singh · Answer

Ans: Hello Student, Please find answer to your question below If the f(x) is decreasing, then ............(1) Also for the domain of logarithm function, &hellip;......(2) Combining (1) and (2) we have Since x belong to R,

Bharat Makkar · Answer

but i think a > 4 as a =3 doesnt satisfy the equation.

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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 ) = log_1/3 ( log₃ ( sin x + a) ) , THEN FIND THE INTERVAL OF ‘’a’’ SO THAT f ( x ) IS DECREASING FOR ALL REAL VALUES OF x .

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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 .

2 Answers

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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 ) = log_1/3 ( log₃ ( sin x + a) ) , THEN FIND THE INTERVAL OF ‘’a’’ SO THAT f ( x ) IS DECREASING FOR ALL REAL VALUES OF x .