G 4. Determine which of the following functions are even, which are odd, and which are neither. (a) f(x) = x 3 + 3x (b) f(x) = 4 sin 2x (c) f(x) = x 2 + |x| (d) f(x) = e x (e) f…

Question

asked Apr 23, 2020 13.0k views

1 Answer

Dan Nguyen · Answer 1 · 2020-04-28T23:03:38+0000

Answer:Given below

Explanation:

A function is said to be odd if

$F\left ( x\right )=F\left ( -x\right )$

(a)
$F\left ( x\right )=x^3+3x$

$F\left ( -x\right )=-x^3-3x=-\left ( x^3+3x\right )$

odd function

(b)
$F\left ( x\right )=4sin2x$

$F\left ( -x\right )=-4sin2x$

odd function

(c)
$F\left ( x\right )=x^2+|x|$

$F\left ( -x\right )=\left ( -x^2\right )+|-x|=x^2+|x|$

even function

(d)
$F\left ( x\right )=e^x$

$F\left ( -x\right )=e^(-x)$

neither odd nor even

(e)
$F\left ( x\right )=(1)/(x)$

$F\left ( -x\right )=-(1)/(x)$

odd

(f)
$F\left ( x\right )=(1)/(2)\left ( e^x+e^(-x)\right )$

$F\left ( -x\right )=(1)/(2)\left ( e^(-x)+e^(x)\right )$

even function

(g)
$F\left ( x\right )=xcosx(h)$

$F\left ( -x\right )=-xcosx(h)$

odd function

(h)
$F\left ( x\right )=(1)/(2)\left ( e^x-e^(-x)\right )$

$F\left ( -x\right )=(1)/(2)\left ( e^(-x)+e^(x)\right )$

odd function