Question

Question For the functions f(x)=9x^(2)+8x+2 and g(x)=4x^(2), find (f+g)(x) and (f+g)(-2).

Answer 1

To find (f+g)(x), add the coefficients of the like terms in f(x) and g(x). Substitute x = -2 to find (f+g)(-2).

Step-by-step explanation:

To find (f+g)(x), we need to add the functions f(x) and g(x). Simply add the coefficients of the like terms. For example, the coefficient of x^2 in f(x) is 9 and in g(x) it is 4. Therefore, the coefficient of x^2 in (f+g)(x) is 9+4=13. Similarly, add the coefficients of x and the constants. The sum of f(x) and g(x) is:

(f+g)(x) = 13x^2 + 8x + 2

To find (f+g)(-2), substitute x = -2 into the equation:

(f+g)(-2) = 13(-2)^2 + 8(-2) + 2 = 13(4) - 16 + 2 = 52 - 16 + 2 = 38