Question 59471
Here's a problem set I did for someone else a couple of days ago.  The last few are composite functions.
:
Use the functions {{{f(x)=2x+7}}}, {{{g(x)=x^2+3x}}}, and {{{h(x)=1/(x-7)}}} to find each of the following.

(1) (f + g) (-1)
{{{(f+g)(x)=(2x+7)+(x^2+3x)}}}
{{{(f+g)(x)=x^2+5x+7}}}
{{{(f+g)(-1)=(-1)^2+5(-1)+7}}}
{{{(f+g)(-1)=1-5+7}}}
{{{highlight((f+g)(-1)=3)}}}
:
(2) (g - f) (x)
{{{(g-f)(x)=(x^2+3x)-(2x+7)}}}
{{{(g-f)(x)=x^2+3x-2x-7}}}
{{{highlight((g-f)(x)=x^2+x-7)}}}
:
(3) (fh)(0)
{{{(fh)(x)=(2x+7)*((1/(x-7)))}}}
{{{(fh)(x)=(2x+7)/(x-7)}}}
{{{(fh)(0)=(2(0)+7)/(0-7)}}}
{{{(fh)(0)=(0+7)/(0-7)}}}
{{{(fh)(0)=7/-7}}}
{{{highlight((fh)(0)=-1)}}}
:
(4) (g o f) (-1)=g(f(-1))
f(-1)=2(-1)+7
f(-1)=-2+7
f(-1)=5
g(f(-1))=g(5)
g(5)=(5)^2+3(5)
g(5)=25+15
g(5)=40
{{{highlight((gof)(x)=40)}}}
:
(5) (f o f) (0)=f(f(0))
f(0)=2(0)+7
f(0)=0+7
f(0)=7
f(f(0))=f(7)
f(7)=2(7)+7
f(7)=14+7
f(7)=21
{{{highlight((fof)(0)=21)}}}
:
(6) (g/f) (4)
{{{(g/f)(x)=(x^2+3x)/(2x+7)}}}
{{{(g/f)(4)=((4)^2+3(4))/(2(4)+7)}}}
{{{(g/f)(4)=(16+12)/(8+7)}}}
{{{highlight((g/f)(4)=28/15)}}}
:
(7) (g o h) (1/2)=g(h(1/2))
{{{h(1/2)=1/(1/2-7)}}}
{{{h(1/2)=1/(1/2-14/2)}}}
{{{h(1/2)=1/(-13/2)}}}
{{{h(1/2)=-2/13}}}
g(h(1/2))=g(-2/13)
{{{g(-2/13)=(-2/13)^2+3(-2/13)}}}
{{{g(-2/13)=4/169-6/13}}}
{{{g(-2/13)=4/169-78/169}}}
{{{g(-2/13)=-74/169}}}
{{{highlight((goh)(1/2)=-74/169)}}}
:

(8) (f o g o h) (8)=(fog)(h(8))
{{{h(8)=1/(8-7)}}}
{{{h(8)=1/1}}}
{{{h(8)=1}}}
(fog)(h(8))=(fog)(1)=f(g(1))
{{{g(1)=(1)^2+3(1)}}}
{{{g(1)=1+3}}}
{{{g(1)=4}}}
f(g(1))=f(4)
f(4)=2(4)+7
f(4)=8+7
f(4)=15
{{{highlight((fogoh)(8)=15)}}}
:
Happy Calculating!!!