Question

How do you find the compositions given `f(x)=x+2` and `g(x)= sqrtx`?

Answer 1

`f(g(x))=sqrt(x)+2`

`g(f(x))=sqrt(x+2)`

Explanation:

It can be confusing to have `x` appear in both base equations; so it might help to convert `f(x)` to `f(a)`
`color(white)("XXX")f(x)=x+2color(white)("XXX")rarrcolor(white)("XXX")f(a)=a+2`
It then becomes easier to think of replacing `a` with `g(x)`
`color(white)("XXX")f(g(x))=g(x)+2 = sqrt(x)+2`

Similarly to evaluate `g(f(x))`

Note you may encounter the following:
`color(white)("XXX")f(g(x))` written as `fog(x)`
and
`color(white)("XXX")f(f(x))` written as `gof(x)`
Use whichever form you or your instructor prefer.