Question

What is `(g@f)(40)` when `f(x) = (x-4)/6` and `g(x) = 4x+6`?

Answer 1

`(g@f)((40)=30`

Explanation:

`(g@f)(x)` can be written as `g(f(x))` and, personally, I find this easier to understand, so...

replacing the variable `x` in the two equations with other variables to help avoid confusion:
`color(white)("XXX")f(color(red)(s))=(color(red)(s)-4)/6`

`color(white)("XXX")g(color(blue)(t))=4color(blue)(t)+6`

So replacing `color(blue)(t)` with `color(blue)(f(40))`
`color(white)("XXX")g(color(blue)(f(40)))=4(color(blue)(f(40)))+6`

then replacing `f(color(red)(40))` with `(color(red)(40)-4)/6`
`color(white)("XXX")g(f(color(red)(40))) = 4((color(red)(40)-4)/6)+6`

Simplifying
`color(white)("XXX")g(f(x)) = 30`