Answer:
a) To find (f + g)(x), we need to add the two functions f(x) and g(x).
(f + g)(x) = f(x) + g(x)
Substituting the given functions, we get:
(f + g)(x) = (3 - x) + (2x + 1)
Simplifying the expression, we have:
(f + g)(x) = 3 - x + 2x + 1
Combining like terms, we get:
(f + g)(x) = 3 + x + 1
(f + g)(x) = x + 4
b) To find (f - g)(x), we need to subtract the function g(x) from f(x).
(f - g)(x) = f(x) - g(x)
Substituting the given functions, we get:
(f - g)(x) = (3 - x) - (2x + 1)
Simplifying the expression, we have:
(f - g)(x) = 3 - x - 2x - 1
Combining like terms, we get:
(f - g)(x) = 3 - 3x - 1
(f - g)(x) = -3x + 2
c) To find (f • g)(x), we need to multiply the two functions f(x) and g(x).
(f • g)(x) = f(x) • g(x)
Substituting the given functions, we get:
(f • g)(x) = (3 - x) • (2x + 1)
Multiplying the expression using the distributive property, we have:
(f • g)(x) = 6x + 3 - 2x^2 - x
Rearranging the terms in descending order of degree, we get:
(f • g)(x) = -2x^2 + 5x + 3
d) To find (f/g)(x), we need to divide the function f(x) by g(x).
(f/g)(x) = f(x) / g(x)
Substituting the given functions, we get:
(f/g)(x) = (3 - x) / (2x + 1)
Since division of polynomials is more complex, we will leave the expression as it is.
Explanation: