Hello from MrBillDoesMath!
The function is continuous on (1,7)
See attached graph. The discontinuity in the function occurs when
3x + 1 =0 =>
x = - (1/3)
but that x value does not lie in the interval (1.7). So there is no discontinuity on (1,7).
FYI: the discontinuity at -1/3 is a non-removable discontinuity
the answer is 8/21
sorry, but im pretty sure its a now that i look at it