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classify each function as even, odd, or neither even nor odd.

 

f(x) = x^6-x^4    even odd or neither

 

g(x) = x^5 -x^4  even odd or neither

 

h(x) = x^5 -x^3  even odd or neither

 Apr 10, 2019
 #1
avatar+109559 
+1

If   f(x)  =  f(-x)   ⇒  even

If   f((-x) = -f(x)  ⇒  odd

Else...neither

 

So

f(x)  =  x^6 - x^4

f(-x)  = (-x)^6 - (-x)^4     =  x^6  -  x^4   =  f(x)  ....so even

 

f(x) = x^5 - x^(4)......neiher even nor odd because

f(-x)  = (-x)^5 - (-x)^4  =  -x^5 - x^4     .....not equal to f(x)

-f(x)  = - [ x^5 - x^4]  =  -x^5 + x^4......not equal to f(-x)

 

f(x)  =  x^5 - x^4

f(-x)  = (-x)^5 - (-x)^3  =  -x^5 + x^3.....not = to f(x)....so....not even

-f(x)  =  - [ x^5 - x^3 ]  =  -x^5 + x^3   =  f(-x).....so....odd

 

 

cool cool cool

 Apr 10, 2019

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