Question

If ƒ(x) = x + 2 and g(x) = 3x2 + 7x, find (f.g)(x)

Answer 1

This is about composite functions, where the second function
$g(x) = 3 {x}^{2} + 7x$
becomes an input for the first function
$f(x) = x + 2$
That is,
$(f \circ \: g)(x) = f(x) \circ g(x)$



$(f \circ \: g)(x) = f(g(x))$

$\rightarrow \: (f \circ \: g)(x) = f(3x {}^{2} + 7x)$



$(f \circ \: g)(x) = (3 {x}^{2} + 7x) + 2$

$\therefore \: (f \circ \: g)(x) = 3x {}^{2} + 7x + 2$