Find the domain of the function.
-$$f ( x ) = \log _ { 4 } ( 3 x + 4 )$$
A) $\left( - \frac { 4 } { 3 } , \infty \right)$
B) $( 0 , \infty )$
C) $\left[ - \frac { 4 } { 3 } , \infty \right)$
D) $\left( \frac { 4 } { 3 } , \infty \right)$

Question

Quizplus · Accepted Answer

For the logarithmic function $\log_4(3x + 4)$ to be defined, the argument $3x + 4$ must be greater than 0. Thus, we solve the inequality $3x + 4 > 0$, which gives $x > -\frac{4}{3}$. Therefore, the domain is $\left( - \frac { 4 } { 3 } , \infty \right)$.

Find the Domain of the Function f(x)=log⁡4(3x+4)f ( x ) = \log _ { 4 } ( 3 x + 4 )f(x)=log4​(3x+4)

Find the Domain of the Function $f ( x ) = \log _ { 4 } ( 3 x + 4 )$