Given the functions, f(x) = x3 + x2 + 1 and g(x) = -6x2 + 2, perform the indicated operations. When applicable, state the domain restriction.(f + g)(x)x3 + 7 x2 + 3x3 - 7 x2 + 5x3 - 5 x2 + 3x3 + 5 x2 + 3
Question
Given the functions, f(x) = x3 + x2 + 1 and g(x) = -6x2 + 2, perform the indicated operations. When applicable, state the domain restriction.(f + g)(x)x3 + 7 x2 + 3x3 - 7 x2 + 5x3 - 5 x2 + 3x3 + 5 x2 + 3
Solution
To perform the operation (f + g)(x), we need to add the functions f(x) and g(x) together.
First, let's write out the functions f(x) and g(x):
f(x) = x^3 + x^2 + 1 g(x) = -6x^2 + 2
To add the functions, we simply add the corresponding terms:
(f + g)(x) = (x^3 + x^2 + 1) + (-6x^2 + 2)
Now, let's simplify the expression by combining like terms:
(f + g)(x) = x^3 + x^2 - 6x^2 + 1 + 2
Combining like terms, we have:
(f + g)(x) = x^3 - 5x^2 + 3
So, the sum of the functions f(x) and g(x) is (f + g)(x) = x^3 - 5x^2 + 3.
As for the domain restriction, there is no specific restriction mentioned in the given question. Therefore, the domain of the sum function (f + g)(x) is the set of all real numbers.
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