Asked by Celene Acuna on Apr 27, 2024
Verified
Find the domain of the rational function. f(x) =xx2−81f ( x ) = \frac { x } { x ^ { 2 } - 81 }f(x) =x2−81x
A) (−∞,0) ∪(0,9) ∪(9,∞) ( - \infty , 0 ) \cup ( 0,9 ) \cup ( 9 , \infty ) (−∞,0) ∪(0,9) ∪(9,∞)
B) (−∞,−9) ∪(−9,9) ∪(9,∞) ( - \infty , - 9 ) \cup ( - 9,9 ) \cup ( 9 , \infty ) (−∞,−9) ∪(−9,9) ∪(9,∞)
C) (−∞,9) ∪(9,∞) ( - \infty , 9 ) \cup ( 9 , \infty ) (−∞,9) ∪(9,∞)
D) (−∞,0) ∪(0,∞) ( - \infty , 0 ) \cup ( 0 , \infty ) (−∞,0) ∪(0,∞)
E) (−∞,∞) ( - \infty , \infty ) (−∞,∞)
Domain
The set of all possible input values (x-values) for which a function is defined.
Rational Function
A function that can be expressed as the quotient of two polynomials.
- Determine and articulate the domain of rational functions.
Verified Answer
FB
Farrah BonnotMay 02, 2024
Final Answer :
B
Explanation :
The denominator x2−81x^2 - 81x2−81 factors to (x+9)(x−9)(x + 9)(x - 9)(x+9)(x−9) , so the function is undefined at x=−9x = -9x=−9 and x=9x = 9x=9 . The domain includes all other real numbers, hence (−∞,−9)∪(−9,9)∪(9,∞)( - \infty , - 9 ) \cup ( - 9,9 ) \cup ( 9 , \infty )(−∞,−9)∪(−9,9)∪(9,∞) .
Learning Objectives
- Determine and articulate the domain of rational functions.