Question

Let f(x) = 2x − 3and g(x) = 3x − 2. what is (f ∘ g)(−2)?

Answer 1

It is given that `f(x) = 2x − 3` and `g(x) = 3x − 2`

we know `color(blue)((f ∘ g)(x)) = f(g(x))`

`color(blue)((f ∘ g)(x)) = f(3x − 2)`

`=>color(blue)((f ∘ g)(-2)) = g(3(-2) − 2)`

`=>color(blue)((f ∘ g)(-2)) = f(-8)`

`=> f(-8) = 2(-8) − 3` `color(white)(wwww` `["as " color(red)(f(x) = 2x − 3)]`

`=>color(blue)((f ∘ g)(-2)) = f(-8) = -19`