Consider the following functions. f(x) = x − 3, g(x) = x2 Find (f + g)(x). Find the domain of (f + g)(x). (Enter your answer using interval notation.) Find (f − g)(x). Find the domain of (f − g)(x). (Enter your answer using interval notation.) Find (fg)(x). Find the domain of (fg)(x). (Enter your answer using interval notation.) Find f g (x). Find the domain of f g (x). (Enter your answer using interval notation.)
Accepted Solution
A:
Answer:1) (f + g)(x) : Domain (-∞, ∞)2) (f - g)(x) : Domain (-∞, ∞)3) (fg)(x) : Domain (-∞, ∞)4) (f×g)(x) : Domain (-∞, ∞)Step-by-step explanation:Since given functions are f(x) = x - 3 and g(x) = x²Then (f + g)(x) = f(x) + g(x) = (x - 3) + x²Since for every of x the given function is defined Therefor, domain of (f + g)(x) will be defined by (-∞, ∞).Since, (f - g)(x) = f(x) - g(x)Now we put the values of f(x) and g(x)(f - g)(x) = (x - 3) - x²Since for every value of x, (f - g)(x) is defined.Therefor, domain of (f - g)(x) will be (-∞, ∞)SInce, (fg)(x) = f [ g(x) ]Now f{ g(x) ] = (x²) - 3 = x² - 3Again this function is defined for every value of x.Therefore, domain of f[ g(x) ] will be (-∞, ∞).At the last we have to find (f×g)(x) = f(x)×g(x) = (x - 3)(x²)Since this function is defined for all values of xTherefore, domain of (f×g)(x) will be (-∞, ∞)