Question

If `f(x)=x^2-x`, how do you find `f(x-6)`?

Answer 1

For every `x` in the equation, we replace it with `x-6`

Explanation:

An easy way to think of `f(x)` is `y`. So `f` is the transformations we apply and whatever comes in the brackets is what we apply the transformations to.

In this case, `f(x)` means `x^2-x`, so we square our `x` value then minus the original `x` from `x^2`. Now, we could put anything in the brackets, and the transformations would be the same - square it then minus the original number from the result.

So the same applies to `f(x-6)`. We simply square `x-6` and then minus `x-6` from the result.

`f(x-6) = (x-6)^2-(x-6) = x^2-12x+36-x+6=x^2-13x+42`

Answer 2

`f(x-6)=x^2-13x+42`

Explanation:

Another way we can do this is to first factor the function `f(x)`.

`f(color(red)x)=color(red)x(color(red)x-1)`

So, when we take the function composition:

`f(color(blue)(x-6))=(color(blue)(x-6))(color(blue)(x-6)-1)=(x-6)(x-7)=x^2-13x+42`