We have: \(f\left(2\right)=5.2+1=11\)

               \(f\left(-1\right)=5.\left(-1\right)+1=-4\)

then: \(a=f\left(2\right)-f\left(-1\right)=11-\left(-4\right)=15\)

Hence: \(g\left(1\right)=a.1+3=15.1+3=18\)