Question

Suppose that the functions h and f are defined as follows h(x)=x^2 +2f(x)=7/9x, x ≠0Find the compositions h• h and f•f Simplify your answers as much as possible (h•h)(x)=(f•f)(x)=

Answer 1

1) First we compute:

$(h\circ h)(x)=h(h(x))=h(x^2+2)=(x^2+2)^2+2.$

Simplifying we get:

$(h\circ h)(x)=x^4+4x^2+4+2=x^4+4x^2+6.$

2)Computing the composition we get:

$(f\circ f)(x)=f(f(x))=f(\frac{7}{9x})=\frac{7}{(9(\frac{7}{9x}))}=\frac{7}{\frac{7}{x}}=x.$

Answer:

$\begin{gathered} (h\circ h)(x)=x^4+4x^2+6, \\ (f\circ f)(x)=x. \end{gathered}$