For which function is f(x) equal to f^1(x) ( answer choices in picture )

C.

Step-by-step explanation:

Let's find the inverse of each of the given options.

Option A:

To find , replace 'x' with 'y' and 'y' with 'x'. This gives,

Rewrite in terms of 'y'. This gives,

The given function

So, option A is incorrect.

Option B:

To find , replace 'x' with 'y' and 'y' with 'x'. This gives,

Rewrite in terms of 'y'. This gives,

The given function

So, option B is incorrect.

Option C:

To find , replace 'x' with 'y' and 'y' with 'x'. This gives,

Rewrite in terms of 'y'. This gives,

The given function

So, option C is correct.

Option D:

To find , replace 'x' with 'y' and 'y' with 'x'. This gives,

Rewrite in terms of 'y'. This gives,

The given function

So, option D is incorrect.

Therefore, only option C is correct.