For what inputs is the expression defined? $$\sqrt { x - 8 }$$
A) $x \geq 7$
B) $x \geq 8$
C) $x \leq 8$
D) $x \geq 1$
E) $x 7$

Question

For what inputs is the expression defined? $$\sqrt { x - 8 }$$
A) $x \geq 7$
B) $x \geq 8$
C) $x \leq 8$
D) $x \geq 1$
E) $x > 7$

Quizplus · Accepted Answer

The expression is defined only if the radicand (the expression under the square root symbol) is non-negative. Thus, we must solve the inequality $x-8\ge 0$ in order to determine for which values of $x$ the expression is defined. Solving $x-8\ge 0$ gives $x\ge 8$. Therefore, the expression is defined for all $x\ge 8$, or in interval notation, $[8,\infty)$. The best answer choice is B, which includes all values of x for which the expression is defined.

For What Inputs Is the Expression Defined x−8\sqrt { x - 8 }x−8​

For What Inputs Is the Expression Defined $\sqrt { x - 8 }$