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`