Question

`f(x) = 2x+6 and g(x) = 4+x`, what is `(f times g)(x)`?

Answer 1

See a solution process below:

Explanation:

`(f xx g)(x) = (color(red)(2x) + color(red)(6))(color(blue)(4) + color(blue)(x))`

To multiply these two terms you multiply each individual term in the left parenthesis by each individual term in the right parenthesis.

`(f xx g)(x) = (color(red)(2x) xx color(blue)(4)) + (color(red)(2x) xx color(blue)(x)) + (color(red)(6) xx color(blue)(4)) + (color(red)(6) xx color(blue)(x))`

`(f xx g)(x) = 8x + 2x^2 + 24 + 6x`

We can now group and combine like terms:

`(f xx g)(x) = 2x^2 + 8x + 6x + 24`

`(f xx g)(x) = 2x^2 + (8 + 6)x + 24`

`(f xx g)(x) = 2x^2 + 14x + 24`