DETERMINE WHETHER EACH OF THE FOLLOWING FUNCTIONS IS EVEN OD

DETERMINE WHETHER EACH OF THE FOLLOWING FUNCTIONS I_S EVEN, ODD, OR NEITHER (a) f(x) = x^4 + 2x^2 (b) g(x) = 7x^3 - x (c) h(x) = x^5 + 1 If f(x) = -2x^2 + x + 5 FIND AND SIMPLIFY THE DIFFERENCE QUOTIENT, f(x+h) - f(x)/h, E or f(x). USE THE GRAPH OF f(x) = x^2 TO GRAPH g(x) = 2(x+3)^2 - 2 BY USING A SEQUENCE OF TRANSFORMATIONS. FIND THE DOMAIN OF EACH FUNCTION IN INTERNATIONAL. (a) f(x) = 5/x^2 + 2x - 8 (b) g(x) = Squareroot x-3/x-6 IF f(x) = 5 - x^2 and g(x) = x^2 + 4x - 12 FIND f + g, f middot g, f/g, AND THE DOMAIN FOR EACH IF f(x) = x^2 + 2 AND g(x) = x^2 - 2 FIND (F middot g)(x) AND (g middot f)(x) AND (g middot f)(-2). IF f(x) = x/x+1 AND g(x) = 4/x FIND (f middot g)(x) AND THE DOMAIN OF (f middot g)(x).

Solution

1)a)f(x)=x⁴+2x²

f(-x)=(-x)⁴+2(-x)²

f(-x)=x⁴+2x²

f(-x)=f(x)

even function

b)g(x)=7x³-x

g(-x)=7(-x)³-(-x)

g(-x)=-7x³+x

g(-x)=-(7x³-x)

g(-x)=-g(x)

odd function

c)h(x)=x⁵+1

h(-x)=(-x)⁵+1

h(-x)=-x⁵+1

neither

2)given f(x)=-2x²+x+5

f(x+h)=-2(x+h)²+(x+h)+5

f(x+h)=-2(x²+2xh+h²)+(x+h)+5

f(x+h)=-2x²-4xh-2h²+x+h+5

difference coefficient =[f(x+h)-f(x)]_/h

difference coefficient =[(-2x²-4xh-2h²+x+h+5)-(-2x²+x+5)]_/h

difference coefficient =[-2x²-4xh-2h²+x+h+5+2x²-x-5]_/h

difference coefficient =[-4xh-2h²+h]_/h

difference coefficient =-4x-2h+1