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  • Please solve RD Sharma class 12 chapter 16 Increasing and Decreasing Function Excercise Very Short Answer type Question 4 Maths Textbook Solution.

Please solve RD Sharma class 12 chapter 16 Increasing and Decreasing Function Excercise Very Short Answer type Question 4 Maths Textbook Solution.

Answers (1)

Answer:

The function is decreasing if  0<a<1

Hint:

If f(x)  is decreasing, then f'(x)<0

Given:

                f(x)=\log a^{x}

Explanation:

It is given that,

                f(x)=\log a^{x}

\Rightarrow         a^{f(x)}=x                                                                                                                            … (i)

Differentiate equation (i) with respect to  x

\Rightarrow         a^{f(x)}\log a=f'(x)=1

\Rightarrow         f'(x)=\frac{1}{a^{f(x)}\log a}

\Rightarrow         f'(x)=\frac{1}{a^{x}\log a}

\Rightarrow         \frac{1}{a^{x}\log a}<0 as   f(x) is decreasing

\Rightarrow         a<1                                                                                                                                    [\because \log 0=1]

Thus, the function is decreasing if  0<a<1

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