The domain of definition of the function f(x) | vedclass

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(D) For the function $f(x) = \frac{3}{4 - x^2} + \log_{10}(x^3 - x)$ to be defined:$1$. The denominator must not be zero: $4 - x^2 
eq 0 \Rightarrow

Vedclass · Accepted Answer

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

Vedclass · Answer

(D) For the function $f(x) = \frac{3}{4 - x^2} + \log_{10}(x^3 - x)$ to be defined:$1$. The denominator must not be zero: $4 - x^2 
eq 0 \Rightarrow x^2 
eq 4 \Rightarrow x 
eq \pm 2$.$2$. The argument of the logarithm must be positive: $x^3 - x > 0$.Factorizing the expression: $x(x^2 - 1) > 0 \Rightarrow x(x - 1)(x + 1) > 0$.Using the wavy curve method (sign scheme) for the critical points $x = -1, 0, 1$,the expression is positive in the intervals $(-1, 0) \cup (1, \infty)$.Combining these conditions,we must exclude $x = 2$ from the interval $(1, \infty)$.Thus,the domain is $(-1, 0) \cup (1, 2) \cup (2, \infty)$.

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

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