Given f(x)=x^2+2x-3, find f^-1(x). If u didnt know f^-1 is basically the inverse of f(x)
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y = x^2 + 2*x - 3
x = y^2 + 2*y - 3
y^2 + 2*y = x + 3
y^2 + 2*y - (x + 3) = 0
a = 1, b = 2, c =- ( x + 3)
b^2 - 4*a*c = 4 - 4*1*( - (x + 3)) = 16 + 4*x
y1 = ( - 2 + sqrt(16 + 4*x))/2 = - 1 + (2/2)*sqrt( 4 + x)
y2 = - 1 - (2/2)*sqrt(4 + x)
f^-1(x) = y = - 1 ± (- sqrt( 4 + x))
x = y^2 + 2*y - 3
y^2 + 2*y = x + 3
y^2 + 2*y - (x + 3) = 0
a = 1, b = 2, c =- ( x + 3)
b^2 - 4*a*c = 4 - 4*1*( - (x + 3)) = 16 + 4*x
y1 = ( - 2 + sqrt(16 + 4*x))/2 = - 1 + (2/2)*sqrt( 4 + x)
y2 = - 1 - (2/2)*sqrt(4 + x)
f^-1(x) = y = - 1 ± (- sqrt( 4 + x))