Answer:
Below in bold.
Step-by-step explanation:
We find fg(x) by replacing the x in f(x) by g(x), so:
fg(x) = (4x - 2a)^2 + 4a(4x - 2a) + a^2
fg(3) = 89 so:
(4(3) - 2a)^2 + 4a(4(3) - 2a) + a^2 = 69
(12 - 2a)^2 + 48a - 8a^2 + a^2 - 69 = 0
144 - 48a + 4a^2 + 48a - 8a^2 + a^2 - 69 = 0
-3a^2 + 75 = 0
-3a^2 = -75
a^2 = 25
a = 5.
Now g(x) = 4x - 2(5) = 4x - 10.
Finding g-1(x);
4x = g(x) + 10
x = (g(x) + 10)/4
So g-1(x) = (x + 10)/4
When g-1(x)= x
x = (x +10)/4
4x = x + 10
3x = 10
x = 10/3.
Break even point is where all the expense is already covered by the revenue. In this case, the expense would be the stand ($75,000) and the lemon+sugar+water ( $1.25 per glass). The revenue comes from lemonade($30/glass). Then the equation would be:
$30 * glass of lemonade= $75,000 + $1.25 * glass of lemonade
($30-$1.25) * glass of lemonade= $75,000
glass of lemonade= 2608.7
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➷ You find the largest value or 'letter' that is shared by both
In this case, you can see the largest common value shared by x^2 and 7x is simply just 'x'
Place 'x' outside the parenthesis and inside the parenthesis place the values you would multiply by x to reach the original expression
Your answer is:
x(x + 7)
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