Is g (x) = 5 + 6/x a linear function?

No it is not linear. The fact that x is in the denominator indicates that it won't be linear. If you graph this out, you'll get a curved hyperbola which is not a straight line.

Linear equations are of the form y = m*x + b where m and b are fixed numbers. For example y = 2*x + 5 is a linear equation (in that case m = 2 and b = 5).