How do you determine if #x sin x# is an even or odd function?
1 Answer
Apr 18, 2016
even function
Explanation:
To determine wether a function is odd/even apply the following.
• If f(x) = f( -x) , then f(x) is even
Even functions are symmetrical about the y-axis.
• If f( -x) = - f(x) , then f(x) is odd
Odd functions have symmetry about the origin.
Test for even
f( -x) = (-x)sin(-x) and sin(-x) = - sinx
#rArr f(-x) = -x.( -sinx )= xsinx = f(x) # thus xsinx is an even function.
This is graph of xsinx. Note symmetry about y-axis.
graph{xsinx [-10, 10, -5, 5]}
