Answer to Question #238310 in Calculus for moe

Question

Consider the following three functions:

(A) $x^2$

(B) $x\cos{x}$

(C) $e^{x}$

and select the correct option for the following:

1. The function (A, B or C) is an even function
2. (A, B or C) is an odd function while the function
3. (A, B or C) is neither odd nor even.

Answer 1

A) $f(x) = x^2$ $f(-x) = (-x)^2=x^2$ -> this is even function

B) $f(x) = xcosx$ $f(-x) = (-x)cos(-x) = -xcosx = -f(x)$ -> this is odd function

C) $f(x) = e^x$ $f(-x) = e^{-x} = \large\frac{1}{e^x}=\frac{1}{f(x)}$ -> this function is neither odd nor even.

1. The function (A, B or C) is an even function (true) A is even function
2. (A, B or C) is an odd function (true) B is odd function
3. (A, B or C) is neither odd nor even. (true) C is neither odd nor even.