What is the domain of $F (x) = \frac{x - 2}{x^{3} + x}$ $F(x)= (x-2)/( x^3+x)$ ?

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Answer 1 · 2017-11-08T02:17:21

Domain: $(- \infty, 0) \cup (0, + \infty)$ $(-oo,0)uu(0,+oo)$

$F (x) = \frac{x - 2}{x^{3} + x}$ $F(x)= (x-2)/(x^3+x)$

$= \frac{x - 2}{x (x^{2} + 1)}$ $= (x-2)/(x(x^2+1))$

$F (x)$ $F(x)$ is defined for all $x$ $x$ except where $x (x^{2} + 1) = 0$ $x(x^2+1) =0$

Since $(x^2+1) >=1 forall x in RR$

$-> F(x)$ is defined $forall x in RR: x!=0$

Hence the domain of $F(x)$ is $(-oo,0)uu(0,+oo)$

As can be deduced from the graph of $F(x)$ below.

graph{(x-2)/(x^3+x) [-10, 10, -5, 5]}

What is the domain of F(x)= (x-2)/( x^3+x)F(x)=x−2x3+xF(x)= (x-2)/( x^3+x)?