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

Question

asked Dec 16, 2022 69.3k views

1 Answer

Leny · Answer 1 · 2022-12-20T22:45:58+0000

Given:

f(x)=(8)/(x)

g(x)=(8)/(x)

To find:

Whether f(x) and g(x) are inverse of each other by using that f(g(x)) = x and g(f(x)) = x.

Solution:

We know that, two function are inverse of each other if:

f(g(x))=x and
g(f(x))

We have,

f(x)=(8)/(x)

g(x)=(8)/(x)

Now,

f(g(x))=f((8)/(x))
$[\because g(x)=(8)/(x)]$

f(g(x))=(8)/((8)/(x))
$[\because f(x)=(8)/(x)]$

f(g(x))=8* (x)/(8)

f(g(x))=x

Similarly,

g(f(x))=f((8)/(x))
$[\because f(x)=(8)/(x)]$

g(f(x))=(8)/((8)/(x))
$[\because g(x)=(8)/(x)]$

g(f(x))=8* (x)/(8)

g(f(x))=x

Since,
and
, therefore, f(x) and g(x) are inverse of each other.