Question

How would I solve this and what would be the answer?

Answer 1

Question:

Solution:

Consider the following functions:

`g(x)=x^2`

and

`h(x)=x-1`

the composition g(g(x)) would be:

`(g\circ g)(x)=g(g(x))=g(x^2)=(x^2)^2=x^4`

then

`(g\circ g)(x)=x^4`

On the other hand, the composition h(h(x)) would be:

`(h\circ h)(x)=h(h(x))=h(x-1)=(x-1)-1=x-1-1=x-2`

then:

`(h\circ h)(x)=x-2`

So that, we can conclude that the correct answer is:

`(g\circ g)(x)=x^4`

and

`(h\circ h)(x)=x-2`