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Question

Find the domain and the range of the following function:
f(x)=x32x+1

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Solution

The function f(x)=x32x+1 is defined only when 2x+10x12
So domain is R{12}
Let y=x32x+1(2x+1)y=x32xy+y=x3y+3=x(12y)x=y+312y
This function is defined only when 12y0y12
So the range is R{12}

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