Question

If h(x) = 4/(5x+2)^2 find two functions f and g such that f(g(x)) = h(x).

Answer 1

We need to find two functions f(x) and g(x) such that f(g(x)) = h(x)

`h(x)=(4)/((5x+2)^2)`

f(g(x)) means the value of f(x) will be evaluated at g(x)

Using trial and error :

Let say :

`f(x)=(4)/(x^2)`

Replacing x as g(x)

`f(g(x))=(4)/((g(x))^2)`

From here, we can say that g(x) = 5x + 2

So we have :

`\begin{gathered} f(x)=(4)/(x^2) \\ g(x)=5x+2 \end{gathered}`