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NDA 2016
Exam
NDA
Year
2016
Subject
Mathematics
Chapter
Functions

NDA 2016 · Mathematics · Functions

Consider the function f(x)= 27( ^ 2 / 3 -x) 4 How many solutions...

Consider the function f(x)=27(\mathrmx2/3−x)4\mathrm{f}(\mathrm{x})=\frac{27\left(\mathrmx^{2 / 3}-\mathrm{x}\right)}{4} How many solutions does the function f(x)=−1f(x)=-1 have?

Options

  1. AOne
  2. BTwo
  3. CThree
  4. DFour

Correct answer

A. One

Step-by-step solution

f(x)=274(x2/3−x)=274((x2)1/3−x)\begin{aligned} f(x) & =\frac{27}{4}\left(x^{2 / 3}-x\right) \\ & =\frac{27}{4}\left(\left(x^2\right)^{1 / 3}-x\right)\end{aligned} Similarly for f(x)=−1f(x)=-1 we will get 27y3−27y2−4=027 y^3-27 y^2-4=0 and after solving it we will find that it has one real solution. y0=1.1184,x=(y0)3=(1.1184)3=1.4\begin{aligned} & y_0=1.1184, \\ & x=\left(\mathrm{y}_0\right)^3=(1.1184)^3=1.4 \end{aligned}
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