Question

Find f(g(x)) and g(f(x)) 1. F(x) = X-5 g(x)=x²-1

Answer 1

Question:

Find f(g(x)) and g(f(x)) 1. F(x) = X-5 g(x)=x²-1​

Solution:

Let f(x) = x-5 and g(x) =x²-1​. Then:

`f(g(x))=f(x^2-1)=(x^2-1)-5=x^2-6`

then, we can conclude that:

`f(g(x))=x^2-6`

On the other hand:

`g(f(x))=g(x-5)=(x-5)^2-1\text{ }`

this is equivalent to:

`=(x^2-2(x.5)\text{ +25)}-1`

this is equivalent to:

`=x^2-10x+25-1=x^2-10x\text{ +24}`

then, we can conclude that:

`g(f(x))=x^2-10x\text{ +24}`

Then, the correct answer is:

`f(g(x))=x^2-6`

and

`g(f(x))=x^2-10x\text{ +24}`