Let f left parenthesis x right parenthesis equals 4 x plus 9 and g left parenthesis x right parenthesis equals 5 x squared. Perform the function operation and then find the domain of the result.

Question

left parenthesis f minus g right parenthesis left parenthesis x right parenthesis

Answer 1

To perform the function operation (f - g)(x), we need to subtract g(x) from f(x):

(f - g)(x) = f(x) - g(x)
(f - g)(x) = (4x + 9) - (5x^2)
(f - g)(x) = 4x + 9 - 5x^2
(f - g)(x) = -5x^2 + 4x + 9

Now, we need to find the domain of the result -5x^2 + 4x + 9.

Since this is a quadratic function, the domain is all real numbers (-∞, ∞).