Given that fx x4 1 and gx x 3 calculate g o gx and g o f

Given that f(x) = x^4 + 1 and g(x) = x + 3, calculate (g o g)(x) and (g o f) of x. Please show your work - how you got to that answer! Thanks!

Solution

f(x) = x^4 + 1 and g(x) = x + 3, calculate (g o g)(x) and (g o f) of x

(g o g)(x)

plug x= g(x) in g(x)

(g o g)(x) = (x+3) +3 = x+6

(g o f)(x)

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

(g o f)(x) =(x^4 +1) +3 = x^4 +4