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>

Question 128610: Let , and

Complete the table

x f(x) g(x) h(x)
-1 -3
-2
12

Answer by jim_thompson5910(35256) (Show Source): You can put this solution on YOUR website!

x	f(x)	g(x)
-1	-3
		-2
	12

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

Start with the second function

Plug in

Multiply

Subtract

So our table becomes

x	f(x)	g(x)
-1	-3	-6
		-2
	12

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

Start with the first function

Plug in

Multiply

Reduce

Now our table updates to

x	f(x)	g(x)
-1	-3	-6
	1	-2
	12

Let's find the third entry of x

Start with the first function

Plug in

Divide both sides by 3 to isolate x

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

x	f(x)	g(x)
-1	-3	-6
	1	-2
4	12

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

Start with the second function

Plug in

Multiply

Subtract

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

x	f(x)	g(x)
-1	-3	-6
	1	-2
4	12	9

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

Start with the given function

Break up the function

Plug in

Plug in , (these values are from the table)

Multiply

Add

x	f(x)	g(x)
-1	-3	-6
	1	-2
4	12	9

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

Start with the given function

Break up the function

Plug in

Plug in , (these values are from the table)

Multiply and reduce

Combine the fractions

x	f(x)	g(x)
-1	-3	-6
	1	-2
4	12	9

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