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

Question

asked Jul 22, 2023 202k views

1 Answer

Bob Herrmann · Answer 1 · 2023-07-26T14:33:31+0000

Question:

Solution:

Consider the following functions:

and

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

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