Question

How do you find [g of h](x) if `g(x)=8-2x` and `h(x)=3x`?

Answer 1

[ g of h ]`(x) = 8-6x`

Explanation:

[g of h]`(x)` can be written as `g(h(x))`

Given `g(color(blue)(x)) = 8 - 2color(blue)(x)`
but the `x` is just a variable place holder and we can replace it with anything we like.

So `g(color(blue)(w)) = 8 - 2color(blue)(w)`
would have identical meanings
as would
`g(color(blue)(h(x))) = 8 -2 color(blue)(h(x)`

Using this last form and replacing color(blue)(h(x)) on the right side with its definition: `color(blue)(h(x)) = color(blue)(3x)`

We have
`g(h(x)) = 8 - 2(color(blue)(3x))`

`color(white)("XXXX")= 8 - 6x`