Question

domain of definition of the function f(x)=3/4-x²+log(x³-x)​

Answer 1

Answer:

$x\in(-1,0)\cup(1,2)\cup(2,\infty)$

Step-by-step explanation:

$4-x^2 ,$ is in the denominator and denominator, can't be equal to zero for any value of x,

thus

$x\neq 2, -2$.............................(1)

Also in  $log(x^3-x)$ logaritham function in defined for values greater than 0,

thus,

$x^3-x>0\\x(x^2-1)>0\\x(x-1)(x+1)>0$

using the wavy curve method,

or simply by checking values of $x(x-1)(x+1)$ in the intervals, sign of the function can be determined(refer figure),

for x(x-1)(x+1) > 0,

$x\in (-1,0)\cup(1,\infty)$...........................(2)

For the domain, both the conditions (1) and (2), must be true,

so,

Domain is $x\in(-1,0)\cup(1,2)\cup(2,\infty)$