Question

Pls help me before I have another mental breakdown

Answer 1

a) fog(x) = (x-2)⁴ +4

b) (g o f) (x) = x⁴ + 2

c) hog(x) =
`√(x-2)`

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)

=
`√(x-2)`

hog(x) =
`√(x-2)`