
Concept explainers
a.
To find the domain of the given rational function.
a.

Answer to Problem 13OE
Domain: (−∞,−1)∪(−1,1)∪(1,∞).
Explanation of Solution
Given:
Rational function: f(x)=x2+1x2−1
Concept used:
To find the domain of the rational function, the following steps are to be followed:
- Equate the denominator equal to zero.
- Solve and find the x values that make the denominator equal to zero.
- The domain is all the real numbers except for those x values equal to zero.
Calculation:
The given rational function is f(x)=x2+1x2−1
The denominator of the given function is x2−1.
Equating the denominator to zero,
⇒x2−1=0
Adding 1 on both sides,
⇒x2−1+1=0+1⇒x2=1
Taking square root on both sides,
⇒√x2=√1⇒x=±1
Hence, the domain of the function is all real numbers except x=±1.
Conclusion:
Therefore, the domain of the function is a (−∞,−1)∪(−1,1)∪(1,∞).
b.
To find the zeros of the function if any.
b.

Answer to Problem 13OE
x=± i
Explanation of Solution
Given:
Rational function: f(x)=x2+1x2−1
Concept used:
To find the zeros of the rational function,
- Equate f(x)=0.
- Simplify and find the values of x which are the zeros of the rational function.
Calculation:
Equate the rational function f(x) to zero.
⇒f(x)=0⇒x2+1x2−1=0
Cross multiplying,
⇒x2+1=(x2−1)(0)⇒x2+1=0
Subtracting 1 on both sides,
⇒x2+1−1=0−1⇒x2=−1
Taking square root on both sides,
⇒√x2=√−1⇒x=± i
Conclusion:
Therefore, the zeroes of the rational function are x=± i .
Chapter 5 Solutions
Algebra and Trigonometry: Structure and Method, Book 2
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