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n
x_2 = 1/x^2
x^1/2 = sqrt(x) x^1/3 = cbrt(x) x^(2/3) = cbrt(x^2)
top is power bottom is root
3
8^4
(3x)^(1/2)
1
sqrt(3x)
1
3x^(-1/2)
3/x^(1/2) = 3/sqrt(x)
(y-2)(y-2) (y^2) -2y -2y +4 (y^2) -4y + 4
12
8
(x+6)(x+2)
(2x-5)(2x+5)
both perfect squares, sqrt each and change the signs
change in y
change in x
rise
run
9 5 + 22 = 27 10-1 = 9 27/9 = 3
3x +b = y -5 = 3(1) + b b = -8
3x-8
3/2x + b = y 3/2(4) + b = 1 6 + b = 1 6 - 5 = 1 3/2x - 5
x
y
2^2 + 3(2) + 10 = 4 + 6 + 10 = 20
(a+1)^2 + 3(a+1) + 10
(a+1)(a+1)+3(a+1)+10
a^2+a+a+1
a^2+2a+1+3(a+1)+10
a^2+2a+1+3a+3+10
a^2+5a+14
(-inf,2)u(2,inf)
[2,inf)
whatever is under the radical has to be positive or 0
sqrt((x^2+2)-1) sqrt(x^2+1)
(sqrt(x-1))^2+2
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