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 log2x 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.