Question

F(x)=1/2x; g(x)=1/3x find f(g(x) and g(f(x) State domain of each Precalculus questions?

Defining New functions Algebraicially

Answer 1

`f(g(x))=1/6x` and `g(f(x))=1/6x`. The domain is `(-oo,oo)`.

Explanation:

`f(x)=1/2x` and `g(x)=1/3x`

To find `f(g(x))`, plug `g(x)` into `f(x)`

`f(g(x))=1/2(1/3x) =1/6x`

To find `g(f(x))`, plug `f(x)` into `g(x)`

`g(f(x))=1/3(1/2x)=1/6x`

The domain of `1/6x` is `(-oo,oo)` because f(x) is defined for all values of x.