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  • Please Solve RD Sharma class 12 chapter 16 Increasing and Decreasing Function Exercise Very Short Answer type Question 10 Maths Textbook solution.

Please Solve RD Sharma class 12 chapter 16 Increasing and Decreasing Function Exercise Very Short Answer type Question 10 Maths Textbook solution.

Answers (1)

Answer:

The given function is decreasing.

Hint:

If  f(x)  is increasing, then  f'(x)>0

If  f(x)  is decreasing, then  f'(x)<0

Given:

                f(x)=\tan ^{-1}g(x)

Where g(x)  is decreasing on  R.

Explanation:

It is given that,

                f(x)=\tan ^{-1}g(x)                                                                                                                                        … (i)

Differentiate equation (i) with respect to x

\Rightarrow         f'(x)=\frac{1}{1+[g(x)]^{2}}g'(x)

Since   g(x)  is decreasing,  g'(x)<0

Also 1+[g(x)]^{2}>0

Thus,  f'(x)<0

Thus, the function is decreasing.

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