Find fx fx fx middot gx fxgx fgx and gfx if defined If an an

Find f(x), f(x), f(x) middot g(x), f(x)/g(x), f(g(x)), and g(f(x)), if defined. (If an answer is undefined, enter UNDEFINED. f(x) = x/x + 3 g(x) = x^5 (a) f(x) + g(x) (b) f(x) - g(x) (c) f(x) middot g(x) (d) f(x)/g(x) (e) f(g(x)) (f) g(f(x))

Solution

a) f(x) + g(x) = x/(x+3) + x^5

b) f(x) - g(x) = x/(x+3) - x^5

c) f(x) .g(x) = x^5 * x / (x+3) = x^6 / (x+3)

d) f(x) / g(x) = x / ( X+3) * x^5   = 1 / (x+3)x^4 = 1 / (x^5 +3x^4)

e) f(g(x) ) = x^5 / ( x^5 + 3)

f) g(f(x)) = [x / ( x+3 )]^5