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Can you help with this question? I'm not sure if the black highlighted choice is right. The question is positive so would it be answer D

Can you help with this question? I'm not sure if the black highlighted choice is right-example-1
User Rajeev Dixit
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1 Answer

13 votes
13 votes

Given the following function:


f(x)=(5x)/(√(3x^2-12))

We will find the domain of the function f(x)

As shown, it is a rational function and there is a square root in the denominator

So, the domain is all real numbers except the values that make the denominator zero or negative

So, we need to solve the following inequality:


3x^2-12>0

We will solve the inequality as follows:


\begin{gathered} 3x^2>12 \\ x^2>(12)/(3) \\ x^2>4 \\ x>2,or,x<-2 \end{gathered}

So, the answer will be

D. all real numbers such that x > 2, x < -2

User Chinabuffet
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