We have the functions:
f(x) = x² and g(x) = x² + 7
So, we can compose them to obtain:
(a)
[tex]\begin{gathered} (f\circ g)(x)=f(g(x))=f(x^2+7)=(x^2+7)^2=(x^2)^2+2\cdot7x^2+7^2 \\ \\ =x^4+14x^2+49 \end{gathered}[/tex]
Since there are no restrictions on the values of x, the domain of this composite function is:
[tex]\mleft\lbrace x\in\mathfrak{\Re }\mright\rbrace[/tex]
In interval notation, this domain can be written as: (-∞, ∞).
