已知定义在$R$上的奇函数$f\left(x\right)$和偶函数$g\left(x\right)$满足$f\left(x\right)+g\left(x\right)=$$a^x-a^{-x}+2$$\left(a>0,且a\ne 0\right)$．若$g\left(a\right)=a$，则$f\left(a\right)=$

2 $\frac{15}{4}$ $\frac{17}{4}$ $a{2}^{}$