How do you know if #g(x) = (x - 1) (x + 3) (1 + x) (3x - 9)# is an even or odd function?

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Answer 1 · 2016-01-14T07:54:13

The explanation is given below.

If #g(-x) = -g(x)# then the function is an odd function
If #g(-x)=g(x)# then the function is an even function

#g(x)=(x-1)(x+3)(1+x)(3x-9)#

#g(x) = (x-1)(x+3)(x+1)(3)(x-3)#

#g(x) = 3(x^2-1)(x^2-9)#

#g(-x)=3((-x)^2-1)((-x)^2-9)#

#g(-x)=3(x^2-1)(x^2-9)#

#g(-x) = g(x)#

Since #g(-x) = g(x)# the function is an even function.