Question

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 f(x)= square root (-x+3)-1

Answer 1

f(x) = (-x + 3)^-1

g(x) = x^-1

h(x) = (-x + 3)

Explanation:

We know that:

g(x) ≠ x

h(x) ≠ x

f(x) = g(h(x))

f(x) = (-x + 3)^(-1) = g(h(x))

Then we can define:

h(x) as the thing inside the first parenthesis:

h(x) = (-x + 3)

And g(x) as the function that is evaluated in this, then:

g(x) = x^-1

So when we have:

g(h(x)) = (h(x))^-1 = ( (-x + 3) )^-1 = (-x + 3)^-1

Then we have:

f(x) = (-x + 3)^-1

g(x) = x^-1

h(x) = (-x + 3)