f(x) and g(x) are polynomials of grade 1. The domain of every polynomial is all real numbers.
a. The addition of two polynomials gives as result a new polynomial, then the domain of f + g is all real numbers, in interval notation: (-∞, ∞)
b. The subtraction of two polynomials gives as result a new polynomial, then the domain of f - g is all real numbers, in interval notation: (-∞, ∞)
c. The multiplication of two polynomials gives as result a new polynomial, then the domain of f * g is all real numbers, in interval notation: (-∞, ∞)
d. The multiplication of two polynomials gives as result a new polynomial, then the domain of f * f is all real numbers, in interval notation: (-∞, ∞)
e. The domain of f/g is all real numbers, except those numbers that make g(x) = 0, that is,
g(x) = 4 - 3x
0 = 4 - 3x
3x = 4
x = 4/3
Then, the domain in interval notation is: (-∞, 4/3) U (4/3, ∞)
f. The domain of g/f is all real numbers, except those numbers that make f(x) = 0, that is,
f(x) = 5x+7
0 = 5x + 7
-7 = 5x
-7/5 = x
Then, the domain in interval notation is: (-∞, -7/5) U (-7/5, ∞)
