To determine the type of filter shown in the circuit and calculate the cut-off frequency, let's analyze the given circuit step-by-step.

The circuit presented is a configuration involving a capacitor \( C \) and resistor \( R_1 \) at the input side, connected to an operational amplifier. This setup suggests a typical high pass filter configuration.

1. In a high pass filter, the capacitor \( C \) blocks any low-frequency signal until the frequency is sufficiently high for the capacitor to allow it through, thereby 'passing' high frequencies while attenuating low frequencies.
2. The input capacitor \( C \) and the resistor \( R_1 \) together form the initial filtering stage.
3. The operational amplifier (op-amp) is configured to boost the signal, ensuring that only frequencies above the calculated cutoff frequency (\( f_{3dB} \)) are significantly affected.

Cut-off Frequency Calculation:

The cut-off frequency for a high pass filter can be calculated using the formula:

\(f_{3dB} = \frac{1}{2 \pi R_1 C}\)

Since the answer mentions the angular frequency in rad/s, the expression becomes:

\(f_{3dB} = \frac{1}{R_1 C} \text{ rad/s}\)

This matches the correct answer choice:

• High pass filter with \(f_{3dB} = \frac{1}{R_1 C}\) rad/s

Therefore, the given circuit is a high pass filter with the specified cut-off frequency.