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

`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 )`