Answer:
a) fog(x) = (x-2)⁴ +4
b) (g o f) (x) = x⁴ + 2
c) hog(x) = [tex]\sqrt{x-2}[/tex]
Step-by-step explanation:
Step(i):-
Given that the function
f(x) = x⁴+4 , g(x) = x-2 , h(x) = √x
f o g (x) = f(g(x))
= f(x-2)
= (x-2)⁴ +4 (∵ f(x) = x⁴ +4))
fog(x) = (x-2)⁴ +4
Step(ii):-
(g o f) (x) = g(f(x))
= g(x⁴ +4)
= x⁴ +4 -2 ( ∵ g(x) = x-2)
= x⁴ + 2
(g o f) (x) = x⁴ + 2
Step(iii):-
hog(x) = h(g(x))
= h(x-2)
= [tex]\sqrt{x-2}[/tex]
hog(x) = [tex]\sqrt{x-2}[/tex]