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  • Please solve RD Sharma class 12 chapter 16 Increasing and Decreasing Function Excercise Very short Answer type Question 3 Maths Textbook Solution.

Please solve RD Sharma class 12 chapter 16 Increasing and Decreasing Function Excercise Very short Answer type Question 3 Maths Textbook Solution.

Answers (1)

Answer:

                The set of values of  a for the given function is  a>1

Hint:

If f(x)  is increasing, 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         \frac{1}{a^{x}\log a}>0 as  f(x) is increasing

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

So the function is increasing if  a>1

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