Question

Please help me with some methods to do this question. Thanks​

Answer 1

Answer: See below

Explanation:

1. For this first pair, we want to find f(g(x)) and g(f(x)). Seeing this may be intimidating and confusing, but as long as you are clear on what you are plugging in, it won't be as confusing.

f(g(x)) means you are plugging the function g(x) into every x in f(x). So, every time you see an x in f(x), you plug in g(x).

`f(g(x))=(1)/(((7)/(x)+6 )-6)`

`f(g(x))=(1)/((7)/(x) ) =(x)/(7)`

f(g(x))=x/7

g(f(x)) means you are plugging the function f(x) into every x in g(x). So, every time you see an x in g(x), you plug in f(x).

`g(f(x))=(7)/((1)/(x-6) ) +6`

`g(f(x))=7(x-6)+6=7x-42+6=7x-36`

g(f(x))=7x-36

2. This pair applies the same rules as above. To make this response not too long, I won't repeat the explanation from above. I will directly write the steps.

`f(g(x))=(√(x+2) )^2+1`

`f(g(x))=x+2+1=x+3`

f(g(x))=x+3

`g(f(x))=\sqrt{x^(2)+1+2 }`

`g(f(x))=√(x^2+3)`

g(f(x))=√(x²+3)