Suppose the cost of producing x objects was defined by the function $C ( x ) = \frac { 60 x } { \sqrt { 60 x - 10 } }$ What is the domain of the function defined by this equation?
A) $\left( \frac { 1 } { 6 } , \infty \right)$
B) $\left( \infty , \frac { 1 } { 6 } \right]$
C) $\left( x , \frac { 1 } { 6 } \right)$
D) $\left[ \frac { 1 } { 6 } , \infty \right)$

Question

Suppose the cost of producing  x  objects was defined by the function $C ( x ) = \frac { 60 x } { \sqrt { 60 x - 10 } }$ What is the domain of the function defined by this equation?
A) $\left( \frac { 1 } { 6 } , \infty \right)$
B) $\left( \infty , \frac { 1 } { 6 } \right]$
C) $\left( x , \frac { 1 } { 6 } \right)$
D) $\left[ \frac { 1 } { 6 } , \infty \right)$

Quizplus · Accepted Answer

The domain of the function is determined by the values of $x$ for which the function is defined. The denominator $\sqrt{60x - 10}$ must be greater than 0 to avoid division by zero and to keep the square root defined (since the square root of a negative number is not real). Setting $60x - 10 > 0$ gives $x > \frac{1}{6}$. Thus, the domain is all real numbers greater than $\frac{1}{6}$, which is $\left( \frac{1}{6}, \infty \right)$.

Suppose the Cost of Producing X Objects Was C(x)=60x60x−10C ( x ) = \frac { 60 x } { \sqrt { 60 x - 10 } }C(x)=60x−10​60x​

Suppose the Cost of Producing X Objects Was $C ( x ) = \frac { 60 x } { \sqrt { 60 x - 10 } }$