1. Tardigrade
  2. Question
  3. Mathematics
  4. The domain of the function f(x)=(3/4-x2)+log10(x3-x), is

Question Error Report

Thank you for reporting, we will resolve it shortly

Back to Question

Q. The domain of the function $f\left(x\right)=\frac{3}{4-x^{2}}+log_{10}\left(x^{3}-x\right)$, is

Relations and Functions

Solution:

Let $g\left(x\right)=\frac{3}{4-x^{2}}$
$\therefore x \ne \pm 2$
$\therefore D\left(g\left(x\right)\right)=R-\left\{-2,2\right\}$
$h\left(x\right)=log_{10}\left(x^{3}-x\right)$
$\therefore x^{3}-x > 0$
$\Rightarrow x\left(x+1\right)\left(x-1\right) > 0$
image

$\therefore x \in\left(-1, 0\right) \cup\left(1, \infty\right)$
$\therefore $ Domain of $f\left(x\right)$ is $\left(-1, 0\right) \cup \left(1,2\right)\cup\left(2, \infty\right)$.