I need help with this problem

Question

Given f(x) find g(x) and h(x) such that f(x)=g(h(x)) and neither g(x) or h(x) is solely x.

f(x)=square root of -2x+4 +1

Answer 1

h (x)= sqr(-2x+4)

g(x)= x+1

g(h(x)) = sqr(-2x+4) + 1 = f(x)

or

g(x) = sqr(x) + 1

h(x) = -2x+4

g(h(x)) = sqr(-2x+4) + 1 = f(x)

UNLESS you may have meant f(x) = -2x+4 +1 = -2x +5

then h(x)=-2x and g(x) = x+5, g(h(x)) = -2x+5 = -2x+4+1

The way you wrote it, using PEMDAS order of operations,is f(x) =sqr(-2x+4) +1,

and not f(x) =sqr(-2x+4+1)

Answer 2

f(x) = √ (-2x+4) + 1

can choose g (x) = √x + 1

and h (x) -2x+4

Then g (h(x)) = g (-2x+4) = √ (-2x+4) + 1 = f(x)