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:
\(=(2/x)=2/(2/x)\)
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
