Out of the following functions, which would be odd?
#g(x)=-1/2(x+5)^3+2#
#g(x)=2(x-3)^2-8#
#g(x)=-4/x#
#g(x)=sqrt(2x+6)-5#
#g(x)=||-x+5||#
1 Answer
Explanation:
I wrote a tutorial for even and odd functions in which all techniques used here are explained. The techniques described may tell you at a glance whether a function is even or odd, but may not be accepted as reasoning by a teacher. As such, alternate reasoning is also provided in some cases.
#g(x)=-1/2(x+5)^3+2# - Not odd
If we expanded the cubed binomial, we would have a polynomial with both even and odd exponents. This would give us a sum of terms which are even and odd functions, meaning
Alternately, consider the counterexample
#g(x)=2(x-3)^2-8# - Not odd
Similar to the above, expanding the squared binomial would give us at least an
Alternately, consider the counterexample
#g(x)=-4/x# - Odd
This is the product of the constant
Alternately, using the definition of an odd function:
#g(x)=sqrt(2x+6)-5# - Not odd
Consider the counterexample
#g(x)=||-x+5||# - Not odd
Consider the counterexample