Question

How do you find `(g*h)(x)` given `f(x)=x^2-1 and`g(x)=2x-3`and`h(x)=1-4x#?

Answer 1

See the entire solution process below:

Explanation:

`(g * h)(x) = g(x) * h(x) = (2x - 3) * (1 -4x)`

`(g * h)(x) = (color(red)(2x - 3))(color(blue)(1 -4x))`

`(g * h)(x) = (color(red)(2x) xx color(blue)(1)) - (color(red)(2x) xx color(blue)(4x)) - (color(red)(3) xx color(blue)(1)) + (color(red)(3) xx color(blue)(4x))`

`(g * h)(x) = 2x - 8x^2 - 3 + 12x`

`(g * h)(x) = -8x^2 + 2x + 12x - 3`

`(g * h)(x) = -8x^2 + (2 + 12)x - 3`

`(g * h)(x) = -8x^2 + 14x - 3`