Question

For which pairs of functions is (f×g)(x)=x

Answer 1

(fog)(x)= f{g(x)}

for 2nd option, the value is f(2/x)=2/(2/x)=x

Answer 2

Option 2 is correct.

Explanation:

We will evaluate the given functions as:

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

Case1:

`f(x)=x^2\text{and}g(x)=(1)/(x)`

`(fog)(x)=f((1)/(x))=((1)/(x))^2`

Which is not a function because it will not give different values of y for different values of x.

Case2:

`f(x)=(2)/(x)\text{and}g(x)=(2)/(x)`

`(fog)(x)=f((2)/(x))=((2)/((2)/(x)))=x`

This will give different values of y for different values of x

Hence, Option 2 is correct.