# How this Fourier Tranform pairs make sense? (in quantum physics)

Recently I read Principles of Quantum Mechanics written by R.Shankar. I am very confused of a formula about the Fourier Transfom in page 68.

The $|k\rangle$ is defined as $|k\rangle\ \leftrightarrow \frac{1}{(2\pi)^{1/2}}e^{ikx}$.

Talking about the pure mathematical definition, the fourier transform pair is correct. But I am confused at $\langle x|f\rangle$ should be $\langle x|k\rangle\langle k|f\rangle$ in the second formula.

EDIT: I have two books.

First is printed second edition. The second formula is $\langle k|x\rangle\langle k|f\rangle$

Second is the picture above.. It is an e-book, also second edition.

Oh, please tell me which one is right.

$$\langle x | k \rangle \langle k | f \rangle$$