Tag: composite functions

Questions Related to composite functions

Let $f\left( x \right) =1+\sqrt { x } $ and $g\left( x \right) =\dfrac { 2x }{ { x }^{ 2 }+1 } $, then

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

  1. $dom(f+g)=(0,\infty)$

  2. range of $f\bigcap$ range of $g=\left{1\right}$

  3. range of $f\bigcup$ range of $g=\left[ -1,\infty \right] $

  4. $All\ of\ the\ above$

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Correct Option: A

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

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

  1. -3

  2. -2$\sqrt { 2 } $

  3. 2$\sqrt { 2 } $

  4. 3

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Correct Option: B