To determine

To find: Find the domain of the function g.

Answer

The domain of the function is 0,∞∪-∞,-3.

Explanation

Calculation:

Given:  gx=log2⁡(x2+3x)

 We know that the function  g is defined whenever x2+3x is positive because domain of log2⁡x is

(0,∞).

Therefore,  x2+3x>0 i.e. xx+3>0⇔x>-3 and x>0, or x<0 and x<-3.

So, the domain of the function is 0,∞∪-∞,-3.

Conclusion: The domain of the function is 0,∞∪-∞,-3.