How do you determine if #g(x) = (4+x^2)/(1+x^4)# is an even or odd function?
1 Answer
Mar 21, 2016
even function
Explanation:
To determine if a function is even/odd the following applies.
• If a function is even then f(x) = f(-x) , for all x
Even functions are symmetrical about the y-axis
• If a function is odd then f(-x) = - f(x)
Odd functions have symmetry about the origin
Test for even :
# g(-x) = (4 + (-x)^2)/(1 + (-x)^4) = (4 + x^2)/(1 + x^4) = g(x)" hence even "# Here is the graph of the function. Note symmetry about y-axis.
graph{(4+x^2)/(1+x^4) [-10, 10, -5, 5]}
