Question

Confirm that f and g are inverses by showing that f(g(x)) = x and g(f(x)) = x.

f of x equals two divided by x and g of x equals two divided by x.

Answer 1

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

Answer 2

Yes

Explanation:

Let f of x by equal to 2/x and g of x be equal to 2/x. The function f(g(x)) means that f is of g(x) which is 2/x. Therefore we substitute 2/x into f of g(x) as x:

`=(2/x)=2/(2/x)`

We then know that a fraction divided by a fraction can be changed to a fraction multiplied by the inverse of the fraction that its divided by, therefore:

`=(2/x)=2/(2/x)=2\cdot(x/2)=x`

Therefore f(g(x))=x

We can do the same for g(f(x)):

`=(2/x)=2/(2/x)`

`=(2/x)=2/(2/x)=2\cdot(x/2)=x`

Therefore f and g are inverses