1. Tardigrade
  2. Question
  3. Mathematics
  4. Consider f(x)=x(x2+6 x+8)(x2-6 x+5), g(x)=x2-3 x-10 and h(x)=(f(x)/g(x)), then number of integers not in the range of h(x) are

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Q. Consider $f(x)=x\left(x^2+6 x+8\right)\left(x^2-6 x+5\right), g(x)=x^2-3 x-10$ and $h(x)=\frac{f(x)}{g(x)}$, then number of integers not in the range of $h(x)$ are

Relations and Functions - Part 2

Solution:

$h(x)=\frac{x(x+2)(x+4)(x-5)(x-1)}{(x-5)(x+2)}$
$h(x)=x(x+4)(x-1), x \neq 5,-2$
image
Clearly $h(-2)$ is contained in range of $h$ but $h(5)$ is not contained in range of $h$.