To find (f+g)(x), we simply add the two functions together:
(f+g)(x) = f(x) + g(x) = (-8x^2 + x - 8) + (9x + 5) = -8x^2 + 10x - 3
The domain of (f+g)(x) is the set of all real numbers since there are no restrictions on the domain of addition. So the domain is (-∞, ∞).
To find (f-g)(x), we subtract g(x) from f(x):
(f-g)(x) = f(x) - g(x) = (-8x^2 + x - 8) - (9x + 5) = -8x^2 + x - 9x - 13 = -8x^2 - 8x - 13
The domain of (f-g)(x) is also the set of all real numbers. So the domain is (-∞, ∞).
To find (f*g)(x), we multiply f(x) and g(x):
(f*g)(x) = f(x)*g(x) = (-8x^2 + x - 8) * (9x + 5) = -72x^3 - 20x^2 + 9x^2 + 63x + 45x + 40 = -72x^3 - 11x^2 + 108x + 40
The domain of (f*g)(x) is again the set of all real numbers. So the domain is (-∞, ∞).
To find (f/g)(x), we divide f(x) by g(x):
(f/g)(x) = f(x)/g(x) = (-8x^2 + x - 8) / (9x + 5)
The domain of (f/g)(x) is the set of all real numbers except for the values of x that make the denominator equal to zero, since division by zero is undefined. So we need to find the values of x that make (9x + 5) = 0:
9x + 5 = 0
9x = -5
x = -5/9
Therefore, x = -5/9 is not in the domain of (f/g)(x).
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+x-8 and g(x)=9x+5
(f+g)(x)=
d=
(f-g)(x)=
d=
(fg)(x)=
d=
(f/g)(x)=
d=
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