Tag: composition of functions and inverse functions

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Questions Related to composition of functions and inverse functions

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.