Question

Find f(x)+g(x),f(x)−g(x),f(x)⋅g(x),f(x)/g(x),f(g(x)), and g(f(x)), if defined. (If an answer is undefined, enter UNDEFINED.) f(x)=x²+6 g(x)= 5−x ​(a) f(x)+g(x) __________ (b) f(x)−g(x) _________ (c) f(x)⋅g(x) ________ (d) g(x)/f(x)__________ ​(e) f(g(x))_______ (f) g(f(x))________

Answer 1

(a) To find f(x)+g(x), substitute the functions f(x) and g(x) into the expression and simplify: (x²+6) + (5-x) = x² + 6 + 5 - x = x² - x + 11.

(b) To find f(x)-g(x), substitute the functions f(x) and g(x) into the expression and simplify: (x²+6) - (5-x) = x² + 6 - 5 + x = x² + x + 1.

(c) To find f(x)⋅g(x), substitute the functions f(x) and g(x) into the expression and simplify: (x²+6) * (5-x) = 5x² - x³ + 30 - 6x = -x³ + 5x² - 6x + 30.

(d) To find g(x)/f(x), substitute the functions f(x) and g(x) into the expression and simplify: (5-x) / (x²+6) = (5-x) / (x²+6).

(e) To find f(g(x)), substitute the function g(x) into f(x) and simplify: f(5-x) = (5-x)² + 6 = 25 - 10x + x² + 6 = x² - 10x + 31.

(f) To find g(f(x)), substitute the function f(x) into g(x) and simplify: g(x²+6) = 5 - (x²+6) = -x² - 1.

Note: Please double-check the calculations as there may be errors.