which of the following is an even function with domain = (reals)? a. 1/(x^2-4) b. e^x^3+1 c. e^x^2-x^2 d. e^x^2-x e. ln x^2

Expert Answers
embizze eNotes educator| Certified Educator

An even function has a graph that is a mirror reflection across the y-axis. For the function, f(-x)=f(x).

(a) `f(x)=1/(x^2-4)` ; `f(-x)=1/((-x)^2-4)=1/(x^2-4)=f(x)` even

(b) `f(x)=e^(x^3)+1` ;`f(-x)=e^((-x)^3)+1=e^(-x^3)+1!=f(x)`

not even. (Nor odd.)

(c) `f(x)=e^(x^2)-x^2` ; `f(-x)=e^((-x)^2)-(-x)^2=e^(x^2)-x^2=f(x)` even

(d) `f(x)=e^(x^2)-x` ; `f(-x)=e^((-x)^2)-(-x)=e^(x^2)+x!=f(x)` not even (nor odd.)

(e) `f(x)=ln(x^2)` ; `f(-x)=ln((-x)^2)=ln(x^2)=f(x)` even


Functions (a),(c),and (e) are even.


The graphs:



** The graphing utility in this program will not handle the exponentials. Note that the 2 graphs given are even and are symmetric about the y-axis. **