Question

Given that `f(x)=x^2-4x` and `g(x)=x+3`, what is `(f∘g)(1)`?

Answer 1

`(f@g)(1) = 0`

Explanation:

The notation `(f @ g)(x)` means the same thing as `f(g(x))`, or to insert `g(x)` as the `x` values of `f(x)`.

The `1` that replaces the `x` means that we just need to calculate the value at the end by substituting `1` for `x` inside the new-formed function.

`(f@g)(x) = (x + 3)^2 - 4(x + 3) = x^2 + 6x + 9 - 4x - 12 = x^2 + 2x - 3`

If you want it in factored form, we can say it is equal to `(x + 3)(x -1)`.

Now, `(f@g)(-1) = (1 + 3)(1 - 1) = 0`.

Hopefully this helps!