Question 947948

for {{{f(x)=3x^2+5}}} and {{{g(x)=7x-2}}},

a)
verify:
{{{g(x+2)<>g(x)+g(2)}}}
 {{{7(x+2)-2<>7x-2+7(2)-2}}}
{{{7x+14-2<>7x-2+14-2}}}
{{{7x+12<>7x+10}}}

b)
find {{{(f-g)(x)}}}
{{{(f-g)(x)=f(x)-g(x) }}}
{{{(f-g)(x)=3x^2+5-(7x-2)}}}
{{{(f-g)(x)=3x^2+5-7x+2}}}
{{{(f-g)(x)=f(x)-g(x) =3x^2-7x+7}}}

c) 
using the resulting function in (b), show that 
{{{(f-g)(2)=f(2)-g(2)}}}
{{{3(2)^2-7*2+7=3(2)^2+5-(7(2)-2)}}}
{{{3*4-14+7=3*4+5-(14-2)}}}
{{{12-14+7=12+5-(12)}}}
{{{19-14=17-12}}}
{{{5=5}}}

d)
is {{{(fg)(0)= (f/g)(0)}}}?  explain

{{{(3*0^2+5)(7*0-2)= ((3*0^2+5)/(7*0-2))}}}

{{{(0+5)(0-2)= ((0+5)/(0-2))}}}

{{{(5)(-2)= 5/-2}}}

{{{-10<> 5/-2}}}
both {{{f(x)=3x^2+5}}} and {{{g(x)=7x-2}}} have y-intercept; so, if {{{x=0}}} then {{{f(x)=3x^2+5}}}  will  be equal to  {{{5}}} , and  {{{g(x)=7x-2}}} will  be equal to {{{-2}}}

e)
find {{{(f(x+h)-f(x))/h}}}, {{{h}}} is not equal to {{{0}}}

{{{(3(x+h)^2+5-(3(x+h)^2+5))/h}}}

{{{(3(x^2+2xh+h^2)+5-(3(x^2+2xh+h^2)+5))/h}}}

{{{(3x^2+6xh+h^2+5-(3x^2+6xh+3h^2)+5)/h}}}

{{{(cross(3x^2)+cross(6xh)+cross(h^2)+cross(5)-cross(3x^2)-cross(6xh)-cross(3h^2)-cross(5))/h}}}

{{{0/h}}}

{{{0}}}