Specify the domain for the function. $f ( x ) = \sqrt { x ^ { 2 } + 7 x - 18 }$
A) $D = ( - \infty , - 9 ] \cup [ 2 , \infty )$
B) $D = ( - \infty , - 2 ) \cup ( 9 , \infty )$
C) $D = [ - 9,2 ]$
D) $D = [ 2 , \infty )$

Question

Quizplus · Accepted Answer

Since the function involves the square root of an expression, the domain must be restricted to ensure that the expression within the square root is non-negative. Solving the inequality $x^2+7x-18 \geq 0$ gives $x \in (-\infty, -9] \cup [2,\infty)$. The union of these two intervals gives the domain $D = (-\infty, -9] \cup [2,\infty)$.

Specify the Domain for the Function f(x)=x2+7x−18f ( x ) = \sqrt { x ^ { 2 } + 7 x - 18 }f(x)=x2+7x−18​

Specify the Domain for the Function $f ( x ) = \sqrt { x ^ { 2 } + 7 x - 18 }$