Respuesta :

konrad509
[tex]f(x)=\dfrac{2}{x}\\ g(x)=\dfrac{2}{x}\\\\ f(g(x))=\dfrac{2}{\dfrac{2}{x}}=x\\\\ g(f(x))=\dfrac{2}{\dfrac{2}{x}}=x[/tex]

Answer:

Yes

Step-by-step 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:

[tex]=(2/x)=2/(2/x)[/tex]

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:

[tex]=(2/x)=2/(2/x)=2\cdot(x/2)=x[/tex]

Therefore f(g(x))=x

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

[tex]=(2/x)=2/(2/x)[/tex]

[tex]=(2/x)=2/(2/x)=2\cdot(x/2)=x[/tex]

Therefore f and g are inverses