Capacitive reactance is inversely proportional to frequency — option 3.

The formula.

\(X_{C}=\dfrac{1}{2\pi fC}\)

where f is the frequency in hertz and C the capacitance in farads. Since f appears in the denominator to the first power, doubling the frequency halves the reactance — an inverse, not an inverse-square-root, relation.

Why it behaves so. A capacitor blocks the steady flow of charge but responds to change. At a higher frequency the applied voltage reverses more often, so the plates are charged and discharged more often, and more charge moves through the circuit in each second — that is, the current is larger and the opposition smaller. At the limit :

The contrast with an inductor. Inductive reactance is

\(X_{L}=2\pi fL\)

which rises with frequency. The two therefore oppose each other, and at the frequency where they are equal the circuit is in resonance :

\(f_{r}=\dfrac{1}{2\pi\sqrt{LC}}\)

Where this is used. The blocking of DC and passing of AC is exactly what a coupling capacitor does between amplifier stages, and a bypass capacitor uses the same property to send high-frequency signals to earth while leaving the DC bias untouched. Filters, tuning circuits in radio receivers, and the smoothing capacitor of a power supply all rest on the frequency dependence of X_C.

A note on units. Reactance is measured in ohms, like resistance, but unlike a resistor it dissipates no power — the energy is stored in the electric field and returned to the circuit each cycle.

Hence, the answer is inversely proportional to frequency.