Question

Suppose that the functions f and g are defined as follows.f(x) = x² +78g(x) =3x5x70Find the compositions ff and g9.Simplify your answers as much as possible.(Assume that your expressions are defined for all x in the domain of the composition. You do not have to indicate the domain.)

Answer 1

`\begin{gathered} (f\cdot f)(x)=x^4+14x^2+49 \\ (g\cdot g)(x)=(64)/(9x^2) \end{gathered}`

Step-by-step explanation

We are given the two functions:

`\begin{gathered} f(x)=x^2+7 \\ g(x)=(8)/(3x) \end{gathered}`

To find (f * f)(x), we have to find the product of f(x) with itself.

That is:

`(f\cdot f)(x)=f(x)\cdot f(x)`

Therefore, we have:

`\begin{gathered} (f\cdot f)(x)=(x^2+7)(x^2+7) \\ (f\cdot f)(x)=(x^2)(x^2)+(7)(x^2)+(7)(x^2)+(7)(7) \\ (f\cdot f)(x)=x^4+7x^2+7x^2+49 \\ (f\cdot f)(x)=x^4+14x^2+49 \end{gathered}`

We apply the same procedure to (g * g)(x):

`\begin{gathered} (g\cdot g)(x)=((8)/(3x))((8)/(3x)) \\ (g\cdot g)(x)=(64)/(9x^2) \end{gathered}`

Those are the answers.