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

Answer:

$f(x)=\frac{2}{x}$ and $g(x)=\frac{2}{x}$

Step-by-step 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.

$(f*g)(x) = \frac{2}{\frac{2}{x} }$

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

Solving the expression:

$(f*g)(x) = \frac{2}{\frac{2}{x} }=\frac{2x}{2}=x$

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.