SOLUTION: Let {{{f(x)=3x}}},{{{g(x)=3x-3}}} and {{{h(x)=(f*g)(x)+(f/g)(x)}}} Complete the table <table border="1"><th>x</th><th>f(x)</th><th>g(x)</th><th>h(x)</th><tr><td>-1</td><td>

Algebra ->  Functions -> SOLUTION: Let {{{f(x)=3x}}},{{{g(x)=3x-3}}} and {{{h(x)=(f*g)(x)+(f/g)(x)}}} Complete the table <table border="1"><th>x</th><th>f(x)</th><th>g(x)</th><th>h(x)</th><tr><td>-1</td><td>      Log On


   

Question 128610: Let f%28x%29=3x,g%28x%29=3x-3 and h%28x%29=%28f%2Ag%29%28x%29%2B%28f%2Fg%29%28x%29

Complete the table
xf(x)g(x)h(x)
-1-3  
1%2F3 -2 
 12 109%261%2F3
Answer by jim_thompson5910(35256) About Me  (Show Source):
You can put this solution on YOUR website!
xf(x)g(x)h(x)
-1-3  
1%2F3 -2 
 12 109%26amp%3B1%2F3



Let's find the first entry of g(x)

g%28x%29=3x-3 Start with the second function


g%28-1%29=3%28-1%29-3 Plug in x=1%2F3


g%28-1%29=-3-3 Multiply


g%28-1%29=-6 Subtract


So our table becomes

xf(x)g(x)h(x)
-1-3-6 
1%2F3 -2 
 12 109%26amp%3B1%2F3


Let's find the second entry of f(x)


f%28x%29=3x Start with the first function


f%281%2F3%29=3%281%2F3%29 Plug in x=1%2F3


f%281%2F3%29=3%2F3 Multiply


f%281%2F3%29=1 Reduce



Now our table updates to

xf(x)g(x)h(x)
-1-3-6 
1%2F31-2 
 12 109%26amp%3B1%2F3



Let's find the third entry of x


f%28x%29=3x Start with the first function


12=3x Plug in f%28x%29=12


4=x Divide both sides by 3 to isolate x


x=4


Now plug this value into the last row of the x column

xf(x)g(x)h(x)
-1-3-6 
1%2F31-2 
412 109%26amp%3B1%2F3



Let's find the third entry of g(x)


g%28x%29=3x-3 Start with the second function


g%284%29=3%284%29-3 Plug in x=4


g%284%29=12-3 Multiply


g%284%29=9 Subtract


Now plug this into the last entry of the g(x) column

xf(x)g(x)h(x)
-1-3-6 
1%2F31-2 
4129109%261%2F3




Now let's find the first entry of h(x)

h%28x%29=%28f%2Ag%29%28x%29%2B%28f%2Fg%29%28x%29 Start with the given function


h%28x%29=f%28x%29%2Ag%28x%29%2Bf%28x%29%2Fg%28x%29 Break up the function


h%28-1%29=f%28-1%29%2Ag%28-1%29%2Bf%28-1%29%2Fg%28-1%29 Plug in x=-1


h%28-1%29=-3%2A%28-6%29%2B%28-3%29%2F%28-6%29 Plug in f%28-1%29=-3, g%28-1%29=-6 (these values are from the table)


h%28-1%29=18%2B1%2F2 Multiply


h%28-1%29=37%2F2 Add


xf(x)g(x)h(x)
-1-3-637%2F2
1%2F31-2 
4129109%261%2F3






Now let's find the first entry of h(x)

h%28x%29=%28f%2Ag%29%28x%29%2B%28f%2Fg%29%28x%29 Start with the given function


h%28x%29=f%28x%29%2Ag%28x%29%2Bf%28x%29%2Fg%28x%29 Break up the function


h%281%2F3%29=f%281%2F3%29%2Ag%281%2F3%29%2Bf%281%2F3%29%2Fg%281%2F3%29 Plug in x=1%2F3



h%281%2F3%29=1%2A%28-2%29%2B%281%29%2F%28-2%29 Plug in f%281%2F3%29=1, g%281%2F3%29=-2 (these values are from the table)



h%281%2F3%29=-2-1%2F2 Multiply and reduce


h%281%2F3%29=-5%2F2 Combine the fractions



xf(x)g(x)h(x)
-1-3-637%2F2
1%2F31-2-5%2F2
4129109%261%2F3