jmc

Question

Is f(x) = (x + 1 + x^2)an even function, odd function, or neither? Enter "odd", "even", or "neither".

Accepted Answer

Note that align* -x + 1 + (-x)^2 &= -x + 1 + x^2 &= (-x + 1 + x^2)(x + 1 + x^2)x + 1 + x^2 &= -x^2 + (1 + x^2)x + 1 + x^2 &= 1x + 1 + x^2, align*so align* f(-x) &= (-x + 1 + x^2) &= ( 1x + 1 + x^2 ) &= - (x + 1 + x^2) &= -f(x). align*Thus, f(x) is an odd function.