Question

Confirm that f and g are inverses by showing that f(g(x)) = x and g(f(x)) = x. (2 points)

Answer 1

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

$f(x)= \frac{8}{x}\\g(x)=\frac{8}{x}$

Now, finding f(g(x))

Put x = 8/x in f(x)

$f(g(x)) =\frac{8}{\frac{8}{x} }\\=8\div \frac{8}{x}\\=8 \times \frac{x}{8}\\=x$

So, we get f(g(x))=x

Now, find g(f(x))

Put x = 8/x in g(x)

$g(f(x)) =\frac{8}{\frac{8}{x} }\\=8\div \frac{8}{x}\\=8 \times \frac{x}{8}\\=x$

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