Question

If `g(n) = 3n+2` and `h(n) = n^2 + 2n`, what is `(g@h)(-2)`?

Answer 1

A function composition means to plug one function into the other.

Explanation:

`(g @ h)(n) = g(h(n))`, so `h(n)` is inserted into `g(n)`. The following diagram shows the concept of a composition, if you are more of a spatial learner.

Computing:

`(g @ h)(n) = 3(n^2 + 2n) + 2 = 3n^2 + 6n + 2`

Now, as you learned in your function notation chapter (I'm assuming you hd one), when a number replaces the independent variable (usually x, but `n` in your case), you must evaluate it in the function.

Hence, `(g @ h)(-2) = 3(-2)^2 + 6(-2) + 2 = 12 - 12 + 2 =`2

So, 2 is our final answer.

Hopefully this helps!