if f(x)=square root x and g(x)=x^3+5, find the compositions f o g, g o f, f o f, and g o g.

Question

if f(x)=square root x and g(x)=x^3+5, find the compositions f o g, g o f, f o f, and g o g.

 

Please solve for 

(f o g)(x)

(g o f)(x)

(f o f)(x)

(g o g)(x)

Answer 1

f(g(x)) = √(x³ - 9)

 

g(f(x)) = (√x)³ - 9 = x√x - 9 or x^3/2 - 9

 

f(f(x)) = √(√x) = x^1/4 or ⁴√x

 

g(g(x)) = (x³ - 9)³ - 9 = (x³ - 9)(x³ - 9)(x³ - 9) - 9 = x⁹ - 27x⁶ - 81x³ - 738