[tex]The\: domain\: of\: f\circ f\: is\: all\: Real\: numbers[/tex]
C) Considering that f(x)=x² we can write the composite function f(f(x)) y plugging into the x-variable the function f(x) itself:
[tex]\begin{gathered} f(f(x)) \\ f\mleft(x\mright)=x^2 \\ f(f(x))=(x^2)^2 \\ f(f(x))=x^4 \end{gathered}[/tex]
Now, let's find the Domain. Considering that this is a polynomial function that has no restraints nor discontinuity we can write out the following:
[tex]\begin{gathered} The\: domain\: of\: f\circ f\: is\: all\: Real\: numbers \\ D=\: \mleft(-\infty\: ,\: \infty\: \mright) \end{gathered}[/tex]
