Question

For f(x) = x^2 and g(x) = x^2 + 2, find the following composite functions and state the domain of each

Answer 1

Answer:

$composite \: function \: is \: given \: as \: in \: two \: forms \\ \\ f(g(x))and \: g(f(x)) \: therefore \: f(g(x)) =( x {}^{2} ) {}^{2} + 2 \\ whereas \: g(f(x)) = (x {}^{2} + 2) {}^{2} \\ domain of \: f(x) = x {}^{2} is( \infty - \infty ) \: and \: domain \: of \: g(x) = x {}^{2} + 2 \: is \: also \: ( \infty - \infty )$