Final answer:
To find f(x) + g(x), we add the two functions. To find f(x) - g(x), we subtract g(x) from f(x). To find f(x) * g(x), we multiply the two functions. To find f(x) / g(x), we divide f(x) by g(x) (undefined).
Step-by-step explanation:
To solve the given problem, we need to find the sum, difference, product, and quotient of the two functions f(x) = 3x + 5 and g(x) = -8x - 10.
a. To find f(x) + g(x), we simply add the two functions together:
f(x) + g(x) = (3x + 5) + (-8x - 10) = -5x - 5
b. To find f(x) - g(x), we subtract g(x) from f(x):
f(x) - g(x) = (3x + 5) - (-8x - 10) = 11x + 15
c. To find f(x) * g(x), we multiply the two functions:
f(x) * g(x) = (3x + 5) * (-8x - 10) = -24x^2 - 10x - 40x - 50 = -24x^2 - 50x - 50
d. To find f(x) / g(x), we divide f(x) by g(x). However, we cannot divide by zero, so we need to make sure g(x) is not equal to zero:
-8x - 10 ≠ 0
-8x ≠ 10
x ≠ -5/4
Therefore, the quotient f(x) / g(x) is undefined.
e. The above operations involve polynomials, except for the division which is not a polynomial.