The function for a is (f o g) (x) = 8x^2-10.
Explanation
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I already knew that the g of x is equal to
so I substitute inside of the g of x
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simplify it
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Let x be the first integer, then
:
x + (x+1) + (x+2) + (x+3) + (x+4) + (x+5) = 519
:
6x + 15 = 519
:
6x = 504
:
x = 84
:
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Our sequence is
:
84, 85, 86, 87, 88, 89
:
The third integer is 86
Answer:
2x^2 +2x-4
——————
2x^2-4x+2
Factor out 2 from the expression
2(x^2+x-2)
—————-
2(x^2-2x+1)
Write x as a difference
2(x^2x-x-2)
—————-
2(x^2-2x+1)
Use a^2-2ab+b^2=(ab)^2
2(x^2x-x-2)
—————-
2(x-1)^2
Reduce the fraction with 2
x^2x-x-2
—————-
(x-1)^2
Factor out x from the expression
X*(x^2)-x-2
—————-
(x-1)^2
Factor out negative sign from the expression
X*(x+2)-(x-2)
—————-
(x-1)^2
Factor out x+2 from the expression
(x+2)(x-1)
—————-
(x-1)^2
Simplify the expression
x+2
——
x-1
