Question

How do you find f(g(x)), f(f(x)), g(g(x)), g(f(x)), given `f(x) = x^2` and `g(x) = ln(x)`?

Answer 1

(see below)

Explanation:

Given
`color(white)("XXX")color(blue)(f(x)=x^2)`
`color(white)("XXX")color(red)(g(x)=ln(x)`

`f(color(blue)(f(x))) =color(blue)(f(x))^2 =(color(blue)(x^2))^2=x^4`

`f(color(red)(g(x)))=(color(red)(g(x)))^2 = color(red)(ln(x))^2`

`g(color(blue)(f(x)))=ln(color(blue)(f(x)))=ln(color(blue)(x^2))`

`g(color(g(x)))=ln(color(red)(g(x)))=ln(color(red)(ln(x)))`