Answer:
we can say that f and g are inverses of each other because f(g(x)) = x and g(f(x)) = x
Step-by-step explanation:
We need to confirm that f and g are inverses by showing that f(g(x)) = x and g(f(x)) = x.
We have
[tex]f(x)= \frac{8}{x}\\g(x)=\frac{8}{x}[/tex]
Now, finding f(g(x))
Put x = 8/x in f(x)
[tex]f(g(x)) =\frac{8}{\frac{8}{x} }\\=8\div \frac{8}{x}\\=8 \times \frac{x}{8}\\=x[/tex]
So, we get f(g(x))=x
Now, find g(f(x))
Put x = 8/x in g(x)
[tex]g(f(x)) =\frac{8}{\frac{8}{x} }\\=8\div \frac{8}{x}\\=8 \times \frac{x}{8}\\=x[/tex]
So, we get g(f(x)) = x
Therefore we can say that f and g are inverses of each other because f(g(x)) = x and g(f(x)) = x
