Tag: inverse functions and theorems

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Questions Related to inverse functions and theorems

Multiple choice maths composite functions composition of functions and inverse functions inverse functions and theorems composition of functions and invertible functions

Let f(x) = ${ x }^{ 2 }\quad +\quad \frac { 1 }{ { x }^{ 2 } } \quad and\quad g(x)\quad =\quad -\quad \frac { 1 }{ x } ,\quad x\in R\quad -\quad \left{ -1,0,1 \right} \quad .If\quad h(x)\quad =\quad \frac { f(x) }{ g(x) } ,\quad then\quad the\quad local\quad minimum\quad value\quad of\quad h(x)\quad is\quad :$

  1. -3
  2. -2$\sqrt { 2 } $
  3. 2$\sqrt { 2 } $

  4. 3
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

h(x) = (x^2 + 1/x^2) / (-1/x) = -x^3 - 1/x. To find the local minimum, take the derivative: h'(x) = -3x^2 + 1/x^2. Setting h'(x) = 0 gives 3x^4 = 1, so x^4 = 1/3. This leads to a local minimum value of -2*sqrt(2) at specific points.