Question

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

Answer 1

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