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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)=

Suppose that the functions h and f are defined as follows hxx2 2fx79x x 0Find the compositions h h and ff Simplify your answers as much as possible hhxffx class=

Respuesta :

1) First we compute:

[tex](h\circ h)(x)=h(h(x))=h(x^2+2)=(x^2+2)^2+2.[/tex]

Simplifying we get:

[tex](h\circ h)(x)=x^4+4x^2+4+2=x^4+4x^2+6.[/tex]

2)Computing the composition we get:

[tex](f\circ f)(x)=f(f(x))=f(\frac{7}{9x})=\frac{7}{(9(\frac{7}{9x}))}=\frac{7}{\frac{7}{x}}=x.[/tex]

Answer:

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

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