Determine the domain of the function $f(x)=\ln \left(4 x-x^{2}\right)$
A) $(-\infty, 0) \cup(4, \infty)$
B) (0,4)
C) (-4,0)
D) $(-\infty, 1.39)$
E) $(-\infty, 0) \cup(0,4) \cup(4, \infty)$

Question

Determine the domain of the function $f(x)=\ln \left(4 x-x^{2}\right)$
A) $(-\infty, 0) \cup(4, \infty)$
B)  (0,4) 
C)  (-4,0) 
D) $(-\infty, 1.39)$
E) $(-\infty, 0) \cup(0,4) \cup(4, \infty)$

Quizplus · Accepted Answer

The domain of $f(x) = \ln(4x - x^2)$ is determined by the requirement that the argument of the logarithm, $4x - x^2$, must be greater than zero. Factoring the quadratic expression gives $x(4-x) > 0$, which holds true for $x \in (0, 4)$. This interval is where the expression inside the logarithm is positive, making the logarithm defined.

Determine the Domain of the Function f(x)=ln⁡(4x−x2)f(x)=\ln \left(4 x-x^{2}\right)f(x)=ln(4x−x2) A) (−∞,0)∪(4,∞)(-\infty, 0) \cup(4, \infty)(−∞,0)∪(4,∞)

Determine the Domain of the Function $f(x)=\ln \left(4 x-x^{2}\right)$ A) $(-\infty, 0) \cup(4, \infty)$