Given f(x), find g(x) and h(x) such that f(x)=g(h(x)) and neither g(x) nor h(x) is solely x.

Question

f(x)=2/x−5

Find g(x)

Find h(x)

Answer 1

given f(x) find g(x) and h(x) such that f(x) = g(h(x))

and neither g(x) nor h(x) is solely x

depends on what f(x) equals, it's given, but what is it given as?

let's say f(x) = x^2 +x, then

h(x) could = x+1 and g(x) = x^2 -x -1

g(h(x)) = g(x+1) = (x+1)^2 - x -1 = x^2 +2x +1 -x-1 = x^2 +x = f(x)

but there is no unique solution

endless possibilities even if you know what f(x) equals

Answer 2

g(x)=2/x

h(x) = x - 5

f(x) = g[h(x)] = g(x-5)= 2/(x-5)