Question

Pls help me before I have another mental breakdown

Answer 1

Answer:

a) fog(x) = (x-2)⁴ +4

b) (g o f) (x) = x⁴ + 2

c) hog(x) = $\sqrt{x-2}$

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)

         =  $\sqrt{x-2}$    

 hog(x) = $\sqrt{x-2}$