1. Tardigrade
  2. Question
  3. Mathematics
  4. Let f(x)=x2+4 x-1 and g(x)=|x|. If h(x)=f(g(x))+10, then the range of h(x), is

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Q. Let $f(x)=x^2+4 x-1$ and $g(x)=|x|$. If $h(x)=f(g(x))+10$, then the range of $h(x)$, is

Relations and Functions - Part 2

Solution:

$h(x)=f(g(x))+10=|x|^2+4|x|-1+10=|x|^2+4|x|+9=(|x|+2)^2+5$
Hence range of $h(x)$ is $[9, \infty)$
Minimum value occurs when $x=0$