Let f left parenthesis x right parenthesis equals x minus 9 and g left parenthesis x right parenthesis equals 3 x squared. Perform the function operation and then find the domain of the result.

Question

left parenthesis f plus g right parenthesis left parenthesis x right parenthesis

Answer 1

To perform the function operation (f + g)(x), we need to add f(x) and g(x) together:

f(x) = x - 9
g(x) = 3x^2

(f + g)(x) = (x - 9) + (3x^2)
(f + g)(x) = 3x^2 + x - 9

Now let's find the domain of the function (f + g)(x). The domain of a function is the set of all possible input values (x) for which the function is defined.

Since (f + g)(x) is a polynomial function, it is defined for all real numbers. Therefore, the domain of (f + g)(x) is all real numbers.