Determine algebraically whether the function fx 6x3 2 is ev

Determine algebraically whether the function f(x) = 6x^3 +2 is even odd or neither. Show all work. Given the composite function f(x) find f(-3), f(0), f(5), and f(a^2+5) Find (f - g)(-5), (f +g)(--5)when f(x) - 4x^2 - 2 and g(x) = x + 7.

Solution

(7) f(x) = 6x^(3) + 2
let f(x) = 0
so 6x^(3) + 2 = 0
6x^(3) = -2
x^(3) = -2/6
there for x = [sqrt(3)*i+1]/2*3^(1/3)
= .946
x = -1/3^(1/3)
= -0.6933

(8) given composite function
f(x) = { x+2}
{-6}
{-x+4}
for f(x) = f(-3)
we get
f(-3) = {-3+2} = -1
{-6}
{-(-3)+4} = 7

for f(x) = f(0)
we get
f(0) = {0+2} = 2
{-6}
{-(0)+4} = 4

f(5) = {5+2} = 7
{-6}
{-(5)+4} = -1

f(a^2 +5)) = {(a^(2))+2+5} = {a^2 + 7}
{-6}
{-(a^2 + 2)+4} = -a^2 + 2

(9) f(x) = -4x^(2) - 2 and g(x) = x + 7
for (f-g)(-5) = (-5){-4x^(2) - 2-x-7}
= {20x^(2) + 5x+45}

for (f+g)(-5) = {-4x^(2) - 2+x+7}
= {20x^(2)-5-25}

for (f*g)(-5) = {(-4x^2 - 2)(x+7)}
= {-4x^3 - 28x^2 - 2x -14}{-5}
= {20x^3 + 140x^2 + 10x + 70}

Answer