Question

For which to pairs of function is (f•g) (x) =x

Answer 1

(fog)(x) = f(g(x))

if f(x) = 2/x and g(x) = 2/x

f(g(x)) = [2 /(2/x)]
f(g(x)) = [2 * x/2 ]
f(g(x)) = x .............matching the function

answer is
B. f(x) = 2/x and g(x) = 2/x

Answer 2

`f(x)=(2)/(x)` and
`g(x)=(2)/(x)`

Explanation:

To prove that we have to demonstrate
`(f*g)(x)=x`

This proof is about a composition of functions, where we have to enter one function inside another, in this case,
`g(x)` goes inside
`f(x)`. So if results in
`x`, then will be proved.

`(f*g)(x) = (2)/((2)/(x) )`

As you can see, the composition is to replace
`g(x)` for the variable of
`f(x)`.

Solving the expression:

`(f*g)(x) = (2)/((2)/(x) )=(2x)/(2)=x`

After replacing and applying the composition, we have
`x` as a result. Therefore, we can say that the pair of functions of option B is the answer, because they satisfy the expression given.