Question

Algebra. I don’t even understand what is being asked. Words confusing

Answer 1

We have a function h(x).

We have to come up with two functions that, when compounded, they give as result h(x).

This compounding of two functions can be expressed as:

`(f\circ g)(x)=f(g(x))=h(x)`

This means that when the function g(x) is the argument of f(x), the result is h(x).

The definition of h(x) is:

`h(x)=√(7x^2+9x-74)`

We then can think of a compound function like this: one function is the quadratic equation and the other function is he square root.

Then, we can try with:

`\begin{gathered} f(x)=√(x) \\ g(x)=7x^2+9x-74 \end{gathered}`

Then, if we now apply the compounding we obtain:

`\begin{gathered} (f\circ g)(x)=f(g(x)) \\ (f\circ g)(x)=√(g(x)) \\ (f\circ g)(x)=√(7x^2+9x-74) \\ (f\circ g)(x)=h(x) \end{gathered}`

So the functions proposed are correct.

Answer: f(x) = √x and g(x) = 7x²+9x-74.