Question

How do you find `(fog)(10)` given `f(x)=-9x-9` and `g(x)=sqrt(x-9)`?

Answer 1

`color(red)(-18)`

Explanation:

`(fog)(x)` basically means `f(g(x))` `i.e.` a function obtained by substituting `g(x)` in place of `x` in `f(x)`.

hence in this case,

`(fog)(x) = f(g(x)) = -9*g(x) - 9`
`= -9*sqrt(x-9) - 9 = -9sqrt(x-9)-9`

`therefore` `(fog)(10) = f(g(10)) = -9sqrt(10-9)-9`
`= -9*1-9 = -9-9 = color(red)(-18)`

Another way to do it would have been to first find `g(10)` ant then substitute the value obtained into `f(x)`.
`therefore` `g(10) = sqrt(10-9) = color(red)1`
`therefore` `f(1) = -9*1-9 = 9-9 = color(red)(-18)`