1.

Extend the function f(x)=x^2 + x defined on the interval (0,3) onto the interval(-3, 3) in an even and an odd way.

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Answer :An EVEN extension defines the FUNCTION `phi(x)={{:(,f(x)=x^(2)+x" for "0 le x le 3),(,f(-x)=x^(2)-2" for "-3 le x LT0):}`
An odd EXTENSIONS defines the function
`PSI(x) ={{:(,f(x)=x^(2)+x" for "0 le x le 3),(,-f(x)=-x^(2)+x" for "-3 le x lt 0):}`


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