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Question

Find the domain of definition of the following function:
f(x)=4x|x|+log(x+2)

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Solution

f(x)=4x|x|+log(x+2)
For f(x) to be real and defined,

x+2>0x>2

x|x| must be0.

if x<0
x|x|=2x<0 which is not possible.

If x0

x|x|=0

Therefore, domain of f(x) is x[0,).


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