To find each of the expressions and their respective domains, we'll substitute the functions into the given expressions directly:
1. (f+g)(x) = f(x) + g(x) = (-8x^2+2x-8) + (9x+5) = -8x^2 + 11x - 3
The domain of (f+g)(x) is all real numbers, so its domain is (-∞, ∞).
2. (f-g)(x) = f(x) - g(x) = (-8x^2+2x-8) - (9x+5) = -8x^2 + 2x - 9x -13 = -8x^2 - 7x -13
The domain of (f-g)(x) is all real numbers, so its domain is (-∞, ∞).
3. (fg)(x) = f(x) * g(x) = (-8x^2+2x-8) * (9x+5) = -72x^3 - 32x^2 -40x - 40
The domain of (fg)(x) is still all real numbers, so its domain is (-∞, ∞).
4. (f/g)(x) = f(x) / g(x) = (-8x^2+2x-8) / (9x+5)
The domain of (f/g)(x) is all real numbers except for the values of x that make the denominator zero (since division by zero is undefined). So we need to solve the equation 9x+5=0 to find the excluded values:
9x = -5
x = -5/9
The excluded value is x = -5/9.
Therefore, the domain of (f/g)(x) is (-∞, -5/9) U (-5/9, ∞).
Use the given functions to find each of the following and their respective domains. Do not try to simplify the resulting functions and be sure to write each domain using interval notation.
f(x)=-8x^2+2x-8 and g(x)=9x+5
(f+g)(x)=
d=
(f-g)(x)=
d=
(fg)(x)=
d=
(f/g)(x)=
d=
1 answer