Rational algebraic functions
Answers are for parents and teachers.
1
Find the domain of (x + 4) ÷ (x² − 3x − 10).
(x − 5)(x + 2) = 0 at 5 and −2. Domain R − {−2, 5}.
2
Simplify (x² − 6x + 9) ÷ (x² − 9) and give its domain.
(x − 3)² ÷ ((x − 3)(x + 3)) = (x − 3) ÷ (x + 3). Domain R − {3, −3}.
3
Find the domain and the set of zeros of (x² − 2x − 8) ÷ (x² − 16).
(x − 4)(x + 2) ÷ ((x − 4)(x + 4)). Domain R − {4, −4}. Numerator zeros {4, −2}, minus denominator zeros {4, −4}: zeros {−2}.
4
Solve (x² − 1) ÷ (x + 1) = 3.
Domain R − {−1}. It simplifies to x − 1 = 3, so x = 4, in the domain. Check: 15 ÷ 5 = 3. Solution set {4}.
5
Find a so that the domain of 7 ÷ (x + a) is R − {−2}.
The denominator must be 0 at x = −2: −2 + a = 0, so a = 2.