Question

7. Two functions are defined below.

F(x) = 5x + 1
g(x) = x/5 - 1/5
Which presentation best establishes that the functions are inverse functions?

Answer 1

Given:

The two functions are

`f(x)=5x+1`

`g(x)=(x)/(5)-(1)/(5)`

To find:

The presentation which establishes that the functions are inverse functions.

Solution:

Two functions f(x) and g(x) are inverse of each other, if

`f(g(x))=g(f(x))=x`

We have,

`f(x)=5x+1`

`g(x)=(x)/(5)-(1)/(5)`

Now,

`g(f(x))=(5x+1)/(5)-(1)/(5)`

`g(f(x))=(5x)/(5)+(1)/(5)-(1)/(5)`

`g(f(x))=x`

Similarly,

`f(g(x))=5\left((x)/(5)-(1)/(5)\right)+1`

`f(g(x))=x-1+1`

`f(g(x))=x`

Since,
`f(g(x))=g(f(x))=x`, therefore, the given functions are inverse of each other.

Hence, the correct option is C.