Find functions f and g so that f compositefunction g H Hx

Find functions f and g so that f compositefunction g = H. H(x) = (2x + 4)^5 Choose the correct pair of functions. A. f(x) = x - 4/2, g(x) = 5 squareroot x B. f(x) = 2x + 4, g(x) = x^5 C. f(x) = 5 squareroot x, g(x) = x - 4/2 D. f(x) = x^5, g(x) = 2x + 4

Solution

f o g(x) = H(x)

H(x) = (2x+4)⁵

Simply by options we can conclude that it statisy 4th option

i.e f(x) = x⁵ , g(x) = 2x+4

f o g(x) = f(g(x)) = f(2x+4)= (2x+4)⁵ = H(x)

So option D is the answer