Write the domain of the function in interval notation.Write numbers as integers or simplified fractions. g(x)=2x−3 over 10x2−33x−7

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Write the domain of the function in interval notation.Write numbers as integers or simplified fractions.   g(x)=2x−3 over 10x2−33x−7

Aniqa O&#039;Neill · Accepted Answer

Step 1  To Determine:  Find the domain of given function:  g(x)=2x−310x2−33x−7  Step 2  Explanation:  Domain is the set of all real x, where function is defined.  Given a rational function.  To find the domain of rational function, we need to find the those x, where function is undefined.  If denominator is 0, then the whole fraction is not defined.  So, we will set the denominator 0 and find the x  10x2−33x−7=0  (5x+1)(2x−7)=0  5x+1=0 2x−7=0  5x−1 2x=7  x=−15 x=72  So, both are the zeroes of the denominator.  It means at x=−15 and x=72 given function is undefined.  Domain is all real x except x=−15 and x=72  Step 3  Answer:  Domain:  D:{x∈R:x≠−15 and x≠72}  D:(−∞,−15)∪(−15,72)∪(72,∞)

Write the domain of the function in interval notation.Write numbers as integers

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