C172 pilot reported a communication breakdown with the other aircraft that was taking off resulted in evasive action to avoid a near midair collision while on approach to landing.

Narrative

On an instrument currency flight under the hood with a safety pilot. After holding; I reported established on the inbound course. Then; I was authorized to change frequency to the CTAF at which time we were 10 miles out and I made an initial call of our location and intention to do a low pass over Runway XX. Hearing no response; I commented we should be good with no conflicts. I made a position report at the FAF as I started my descent. At a waypoint which is 2.9 miles from the runway threshold; I made a final call with our intentions. We heard no activity on the radio; which led me to believe we had no conflicts. At that time my safety pilot told me to turn left as there was an aircraft that had just departed on Runway XY. I turned left as he did also.I believe we were on the correct frequency as I had confirmed the frequency when issued the authorization to change to the CTAF frequency. The aircraft is equipped with a Garmin GTN 650Xi as Com1 and a Garmin GNC 225 on Com 2. I was using the GNC 225 to transmit our locations and intentions. The GNC 225 shows an identification of the frequency. Both my safety pilot and I recall that the correct frequency was showing. I used the same radio to obtain the ATIS at ZZZ2 and for ground communication after landing and it worked correctly. I believe the radio was working at the time of the incident. I understand the pilot contacted the FBO where I rent the plane and commented that he made announcements of his intentions for departure Runway XY. We did not hear any transmissions.