The domain of the function $f ( x ) = \sqrt { 2 x + 3 }$ is

A) $( - \infty , \infty )$
B) $\left( - \frac { 3 } { 2 } , \infty \right)$
C) $\left[ - \frac { 3 } { 2 } , \infty \right)$
D) $\left( - \frac { 2 } { 3 } , \infty \right)$
E) $\left[ \frac { 3 } { 2 } , \infty \right)$

Question

The domain of the function $f ( x ) = \sqrt { 2 x + 3 }$ is

A) $( - \infty , \infty )$
B) $\left( - \frac { 3 } { 2 } , \infty \right)$
C) $\left[ - \frac { 3 } { 2 } , \infty \right)$
D) $\left( - \frac { 2 } { 3 } , \infty \right)$
E) $\left[ \frac { 3 } { 2 } , \infty \right)$

Quizplus · Accepted Answer

The domain of a square root function includes all x values for which the expression inside the square root is non-negative. For $f(x) = \sqrt{2x + 3}$, the expression $2x + 3$ must be greater than or equal to 0. Solving $2x + 3 \geq 0$ gives $x \geq -\frac{3}{2}$, which corresponds to the interval $\left[ -\frac{3}{2}, \infty \right)$.

The Domain of the Function f(x)=2x+3f ( x ) = \sqrt { 2 x + 3 }f(x)=2x+3​

The Domain of the Function $f ( x ) = \sqrt { 2 x + 3 }$