Find fog and g o f fx x23 gx x12 fog gof Find the domain o

Find fog and g o f. f(x) = x^2/3, g(x) = x^12 fog gof Find the domain of each function and each composite function. (Enter your answers using interval notation.) domain of f domain of g domain of f o g domain of g o f

Solution

f(x) = x^2/3 ; g(x) = x^12

Domain of f(x) : all real , ( -inf , inf)

Domain of g(x) : all real , ( -inf , inf)

(fog)(x) ; plug x= g(x) in f(x)

(fog)(x) = (x^12)^2/3 = x^8

(gof)(x) : plug x= f(x) in g(x)

(gof)(x) = (x^2/3)^12 = x^8

Domain of (fog)(x) : all real , ( -inf , inf)

Domain of (gof)(x) : all real , ( -inf , inf)