You most likely will have an impedance bump, but perhaps no worse than
that in a standard PL259 connector.
Depends on whether you are going to use the cable on HF or VHF, and
whether it will be exposed to the weather or not.
Here is one approach:
1) Slip a few pieces of heat-shrink tubing over each coax end and slide
it out of the way. (This presumes you have connectors on the other
ends which would prevent you from putting the heat shrink on after
splicing it.)
2) Strip back a couple inches of the outer insulation from each cable and
push back the braid.
3) Strip the inner conductor of the RG-174 for about 1".
4) Slice the inner insulation of the RG-8X on each side and fold it back
to expose the inner conductor (but don't cut it off if you can help it.)
5) Solder the inner conductors together.
6) Reform the inner insulation of the RG-8X over the joint.
7) Tease the RG-174 braid out as needed so it extends over the joint.

Extend the RG-8X braid over the joint. Wrap the braids together
with #24 bare wire and solder CAREFULLY. (My most common problem
using RG-174 is melting the inner insulation when soldering the braid.)
9) Now slip the heat shrink tubing over the joint and shrink it to get a
good mechanical connection. You probably will need several layers of
heatshrink on the RG-174 to bring the outside diameter up close to the
size of the RG-8X before putting a couple longer (and larger diameter)
pieces connecting both cables.
Hint: You may want need more braid length than center conductor.
If so, trim back more of the coax in step 2, then trim back the center
conductors in steps 3 and 4.
If you are using it outside, I would still add additional weather proofing
to the outside of the joint.
Good luck!
- Dale WB6BYU