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  • Provide solution for rd sharma maths class 12 chapter 16 Increasing and decreasing functions exercise multiple choice quection, question 10

Provide solution for rd sharma maths class 12 chapter 16 Increasing and decreasing functions exercise multiple choice quection, question 10

Answers (1)

Correct option (c)

Hint: Differentiate the given function w.r.t  x  then check the given conditions

Given:f(x)=x^{3}-6 x^{2}+15 x+3

Explanation: It is given that

f(x)=x^{3}-6 x^{2}+15 x+3

Now,Differentiate (i) w.r.t  x

\begin{aligned} &f^{\prime}(x)=3 x^{2}-12 x+15 \\ &f^{\prime}(x)=3\left(x^{2}-4 x+5\right) \\ &f^{\prime}(x)=3\left[(x-2)^{2}+1\right]>0 \end{aligned} 

Since \begin{aligned} &f^{\prime}(x)>0 \end{aligned} , so \begin{aligned} &f(x) \end{aligned}  is increasing function.

As \begin{aligned} &f(x) \end{aligned} is increasing, it is invertible

Thus, \begin{aligned} &f(x) \end{aligned} is invertible function.

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