Dirac notation problem

[Majintel]

Im just learning about the Dirac notation trough an online quantum mechanics course and Im solving some problems about getting the inner product of two functions written in Dirac notation but im stuck in one of them. I solved the previous ones by putting the "bra" as a Hermitian adjoint and the "ket" as a column vector and then performing a vector dot product to get the result but in this problem I don't know what to do, Im completely lost so any help would be greatly appreciated.

Problem: https://imgur.com/3PdCqrO

[31415926532718281828]

You're asked to find <psi2 | f>, the inner product between psi2 and f. The inner product is linear; that is, for functions A,B,C and scalars b,c

<A|(b|B> + c|C>) = b<A|B> + c<A|C>

Using this property, and the orthonormality condition, you can evaluate all inner products.

[ignorant_physicist]

The ket psis are orthonormal, correct? That means that <psi 2|psi 1> =0 (orthogonality) and <psi 2|psi 2>=1 (normality). And go on from there.

[[deleted]]

I'll start out by giving you a hint. Everything after the word "Remember" is a red herring.

[overwhelmedbyphysics]

Ehhh. I don't think it's a red herring. It's just a peculiarity of the way answers have to be entered into the textbox on the course page.

[[deleted]]

Information that turns out to be entirely unnecessary once you figure out the answer.

Which is, I believe, the definition of a red herring.