Find the domain of f.
-$$f ( x ) = \sqrt { 9 x + 4 }$$
A) $\left\{ x \mid x \leq - \frac { 4 } { 9 } \right\}$
B) $\left\{ x \mid x \geq \frac { 4 } { 9 } \right\}$
C) $\left\{ x \mid x - \frac { 4 } { 9 } \right\}$
D) $\left\{ x \mid x \geq - \frac { 4 } { 9 } \right\}$

Question

Find the domain of f.
-$$f ( x ) = \sqrt { 9 x + 4 }$$
A) $\left\{ x \mid x \leq - \frac { 4 } { 9 } \right\}$
B) $\left\{ x \mid x \geq \frac { 4 } { 9 } \right\}$
C) $\left\{ x \mid x > - \frac { 4 } { 9 } \right\}$
D) $\left\{ x \mid x \geq - \frac { 4 } { 9 } \right\}$

Quizplus · Accepted Answer

The square root function is defined only for nonnegative (or zero) input, thus we solve the inequality 
$$9 x + 4 \geq 0$$
to find the domain. Subtracting 4 from both sides and then dividing by 9 yields 
$$x \geq - \frac { 4 } { 9 }$$
so the domain is $\left\{ x \mid x \geq - \frac { 4 } { 9 } \right\}$. Therefore, the best choice is D.

Find the Domain of F f(x)=9x+4f ( x ) = \sqrt { 9 x + 4 }f(x)=9x+4​

Find the Domain of F $f ( x ) = \sqrt { 9 x + 4 }$